Plane mensuration

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1. 1Areas of flat shapesRectangles, triangles, parallelograms, trapeziums and rhombuses: where each area formula comes from, and why the height must be perpendicular.Done15 min
2. 2Circles, arcs and sectorsCircumference and area, then arcs and sectors as a fraction θ/360 of the circle, the perimeter of a sector, and working back to the angle or radius.Done15 min
3. 3Segments, chords and composite shapesA segment is a sector minus a triangle: its area, the chord, the perimeter of a segment, and shapes built from rectangles, triangles and parts of circles.Done16 min

Past questions (145)

From 1983–2025: 79 WAEC, 10 NECO, 56 JAMB. Theory questions first, then objective, newest first.

Theory (57)

• WAEC 2024 · Paper 2 · Q3A circular floor of a building is to be tiled with square ceramic tiles, each of side $40\text{ cm}$. If the perimeter of the floor is $66\text{ m}$, …
• WAEC 2024 · Paper 2 · Q9The diameter of a circle centre $O$ is $26\text{ cm}$. A chord $PQ$ is drawn such that its midpoint is $5\text{ cm}$ from $O$. Calculate, correct …
• NECO 2023 · Paper 2 · Q3In the diagram, $O$ is the centre of the circle, the chord $AB$ is $12\text{ cm}$ long and $\angle ACB = 30^\circ$.
• NECO 2023 · Paper 2 · Q6If $135_k = 231_{\text{four}}$, find the value of $k$.
• WAEC 2023 · Paper 2 · Q11Two regular polygons $P$ and $Q$ are such that the number of sides of $P$ is twice the number of sides of $Q$. The difference between the exterior …
• WAEC 2023 · Paper 2 · Q12In the diagram, $P$, $Q$, $R$ and $S$ are points on the circle with centre $O$; $QR \parallel OS$, $\angle QOR = 2m$, $\angle QPR = n$ and $\angle SOR = 54^\circ$. …
• WAEC 2023 · Paper 2 · Q13In the diagram, the radius of the sector of the circle centre $O$ is $7\text{ cm}$ and $\angle MON = 60^\circ$; $NT \perp OM$. Find, correct …
• WAEC 2023 · Paper 2 · Q3In the diagram, $PQR$ is an equilateral triangle of side $18\text{ cm}$. $M$ is the midpoint of $\overline{QR}$. An arc of a circle with centre …
• WAEC 2023 · Paper 2 · Q13$ABCD$ is a trapezium with $\overline{BC} \parallel \overline{AD}$. $E$ is a point on $AD$ such that $\overline{BE} \perp \overline{AD}$. If …
• WAEC 2023 · Paper 2 · Q2If $3$ and $-\frac27$ are the roots of the quadratic equation $px^2 + qx + r = 0$, find the values of $p$, $q$ and $r$.
• NECO 2022 · Paper 2 · Q6Use logarithm tables to evaluate $\sqrt[3]{\left(\frac{565 \times 0.0536}{249.1}\right)^2}$.
• WAEC 2022 · Paper 2 · Q3A chord subtends an angle of $72^\circ$ at the centre of a circle of radius $24.5\text{ m}$. Calculate the perimeter of the minor segment. $\left[\text{Take }\pi = \frac{22}{7}\right]$
• WAEC 2022 · Paper 2 · Q8In the diagram, $|PR| = 20\text{ cm}$, $|PS| = 24.12\text{ cm}$, $\angle PRS = 90^\circ$ and $Q$ is a point on $\overline{PR}$. If $\angle SPQ = 34^\circ$ …
• WAEC 2021 · Paper 2 · Q8In $\triangle PQR$, $\angle PQR = 90^\circ$. If its area is $216\text{ cm}^2$ and $|PQ| : |QR|$ is $3 : 4$, find $|PR|$.
• WAEC 2021 · Paper 2 · Q9In the diagram, $PQRS$ is a trapezium with $\overline{QR} \parallel \overline{PS}$. $U$ and $T$ are points on $\overline{PS}$ such that $|PU| = 5\text{ cm}$, …
• WAEC 2021 · Paper 2 · Q4The sides of a rectangle are $(x + 3)\text{ cm}$ and $(x - 2)\text{ cm}$. If the area of the rectangle is $36\text{ cm}^2$, find its:
• WAEC 2021 · Paper 2 · Q9A tailor had a piece of cloth in the shape of a trapezium. The perpendicular distance between the two parallel edges was $38\text{ cm}$. The …
• WAEC 2020 · Paper 2 · Q12In the diagram, $\overline{AB}$ is a tangent to the circle with centre $O$ and $COEB$ is a straight line. If $\overline{CD} \parallel \overline{AB}$ …
• WAEC 2020 · Paper 2 · Q11The diagram is a circle, centre $O$, with radius $35\text{ cm}$. The arc $MN$ subtends an angle of $120^\circ$ at the centre. Find, correct to …
• WAEC 2020 · Paper 2 · Q4In the diagram, $R$, $S$, $T$, $U$ are points on a circle and $QRS$ is a straight line. $\angle STU = 124^\circ$ and $\angle QUR = 31^\circ$. …
• WAEC 2020 · Paper 2 · Q4The diagram shows a trapezium $ABCD$ in which $\overline{AB} \parallel \overline{DC}$, $|AD| = 7.5\text{ cm}$, $|AB| = 8\text{ cm}$, $|BC| = 6.8\text{ cm}$ …
• WAEC 2020 · Paper 2 · Q8In an isosceles triangle $ABC$, $|AB| = |AC| = 6\text{ cm}$ and $\angle BAC = 130^\circ$. Find, correct to two significant figures, the: …
• WAEC 2019 · Paper 2 · Q4In the diagram, $PQRS$ is a quadrilateral, $\angle PQR = \angle PRS = 90^\circ$, $|PQ| = 3\text{ cm}$, $|QR| = 4\text{ cm}$ and $|PS| = 13\text{ cm}$. …
• WAEC 2019 · Paper 2 · Q7In the diagram, $MN$ is a chord of a circle with centre $O$. If $|MN| = 22.42\text{ cm}$ and the perimeter of triangle $MON$ is $55.6\text{ cm}$, …
• WAEC 2018 · Paper 2 · Q3The diagonals of a rhombus are $10.2\text{ cm}$ and $9.3\text{ cm}$ long. Calculate, correct to one decimal place, the perimeter of the rhombus.
• WAEC 2018 · Paper 2 · Q9In the diagram, $T$ is on $PS$ and $Q$ is on $PR$ with $TQ \parallel SR$. $|PT| = 4\text{ cm}$, $|TS| = 6\text{ cm}$, $|PQ| = 6\text{ cm}$ and …
• WAEC 2018 · Paper 2 · Q3The diagram shows an athletics track with two parallel sides and two semicircular ends. Each of the parallel sides is 60 metres long and the …
• WAEC 2018 · Paper 2 · Q6If $\tan x = \frac{5}{12}$, $0^\circ < x < 90^\circ$, evaluate, without using mathematical tables or a calculator, $\dfrac{\sin x}{(\sin x)^2 + \cos x}$.
• WAEC 2017 · Paper 2 · Q11It takes 8 students two-thirds of an hour to fill 12 tanks with water. How many tanks of water will 4 students fill in one-third of an hour at …
• WAEC 2017 · Paper 2 · Q3The angle of depression of a point $P$ on the ground from the top $T$ of a building is $23.6^\circ$. If the distance from $P$ to the foot of …
• WAEC 2017 · Paper 2 · Q2A trader invested some money in a bank for two years at $5\%$ per annum compound interest. If he collected an amount of ₦2,205,000.00 for his …
• WAEC 2017 · Paper 2 · Q8The probabilities that Akafi and Iniola will pass an examination are $\frac34$ and $\frac35$ respectively. Find the probability that only Iniola …
• WAEC 2016 · Paper 2 · Q11If $\dfrac{3p + 4q}{3p - 4q} = 2$, find $p : q$.
• WAEC 2016 · Paper 2 · Q5In the diagram, $PQST$ is a parallelogram, $PQMR$ is a straight line, $|TS| = 8\text{ cm}$, $|SM| = 6\text{ cm}$ ($SM \perp PR$) and the area …
• WAEC 2016 · Paper 2 · Q5The diagram shows a semicircular arc on a school gate with centre $O$ and diameter $AE$, with a shaded segment $BCD$. If $|AE| = 14$ metres and …
• WAEC 2015 · Paper 2 · Q5A trapezium $PQRS$ is such that $PQ \parallel RS$ and the perpendicular from $P$ to $RS$ is $40\text{ cm}$. If $|PQ| = 20\text{ cm}$, $|SP| = 50\text{ cm}$ …
• WAEC 2014 · Paper 2 · Q10Solve: $(x - 2)(x - 3) = 12$.
• WAEC 2014 · Paper 2 · Q4In the diagram, $O$ is the centre of the circle of radius $r\text{ cm}$ and $\angle XOY = 90^\circ$. If the area of the shaded segment $XKY$ …
• WAEC 2013 · Paper 2 · Q10A segment of a circle is cut off from a rectangular board $22\text{ cm}$ by $12\text{ cm}$ as shown in the diagram, leaving $5\text{ cm}$ and …
• WAEC 2013 · Paper 2 · Q4The area of a circle is $154\text{ cm}^2$. It is divided into three sectors such that two of the sectors are equal in size and the third sector …
• WAEC 2013 · Paper 2 · Q12An open rectangular tank is made from a steel plate of area $1440\text{ m}^2$. Its length is twice its width. If the depth of the tank is $4\text{ m}$ …
• WAEC 2013 · Paper 2 · Q7In the diagram, $PQS$ is a right-angled triangle, $\angle PSQ = 90^\circ$, $|PS| = 3\text{ cm}$, $|PQ| = 5\text{ cm}$, $\angle PRS = 61^\circ$ …
• WAEC 2012 · Paper 2 · Q5In the diagram, $O$ is the centre of the circle and $XY$ is a chord. If the radius is $5\text{ cm}$ and $|XY| = 6\text{ cm}$, calculate, correct …
• WAEC 2012 · Paper 2 · Q11A sector of a circle with radius $20\text{ cm}$ has an area of $396\text{ cm}^2$. Calculate, correct to 1 decimal place, the: $\left[\text{Take }\pi = \frac{22}{7}\right]$
• WAEC 2012 · Paper 2 · Q3In the diagram, $ABCD$ is part of a right-angled triangle $ODC$ (with $A$ on $OD$ and $B$ on $OC$). If $|AB| = 6\text{ cm}$, $|CD| = 15\text{ cm}$, …
• WAEC 2012 · Paper 2 · Q6Simplify: $\left[\dfrac{3m + 1}{6} - \dfrac{m + 2}{5}\right] \div \dfrac{9m - 7}{15}$.
• WAEC 2011 · Paper 2 · Q12The area of trapezium $PQRS$ is $60\text{ cm}^2$. $PQ \parallel RS$, $|PQ| = 15\text{ cm}$, $|RS| = 25\text{ cm}$ and $\angle PSR = 30^\circ$. …
• WAEC 2011 · Paper 2 · Q3A sector of a circle with radius $21\text{ cm}$ has an area of $280\text{ cm}^2$. Calculate, correct to 1 decimal place, the perimeter of the …
• WAEC 2011 · Paper 2 · Q8Given that $\sin x = 0.6$ and $0^\circ \le x \le 90^\circ$, evaluate $2\cos x + 3\sin x$, leaving your answer in the form $\frac mn$, where $m$ …
• WAEC 2010 · Paper 2 · Q11In the diagram, $\angle PTQ = \angle PSR = 90^\circ$, $|PQ| = 10\text{ cm}$, $|PS| = 14.4\text{ cm}$ and $|TQ| = 6\text{ cm}$. Calculate the …
• WAEC 2010 · Paper 2 · Q6The scale of a map is $1 : 20\,000$. Calculate the area, in square centimetres, on the map of a forest reserve which covers $85\text{ km}^2$.
• WAEC 2010 · Paper 2 · Q5The diagonals of a rhombus are $14\text{ cm}$ and $9\text{ cm}$. Calculate, correct to the nearest centimetre, the perimeter of the rhombus.
• WAEC 2010 · Paper 2 · Q8Using ruler and a pair of compasses only:
• WAEC 2009 · Paper 2 · Q11A circle is inscribed in a square. If the sum of the perimeter of the square and the circumference of the circle is 100 cm, calculate the radius …
• WAEC 2009 · Paper 2 · Q8The area of a rectangular football field is $7200\text{ m}^2$ and its perimeter is 360 m.
• WAEC 2008 · Paper 2 · Q11In the diagram, $AB \parallel CD$ and $BC \parallel FE$, $\angle CDE = 75^\circ$ and $\angle DEF = 26^\circ$. Find the angles marked $x$ and …
• WAEC 2008 · Paper 2 · Q5A rectangular field is $l$ metres long and $b$ metres wide. Its perimeter is $280$ metres. If the length is two and a half times its breadth, …

Objective (88)

• WAEC 2025 · Paper 1 · Q22The diagonals $AC$ and $BD$ of a rhombus $ABCD$ are $16\text{ cm}$ and $12\text{ cm}$. Calculate its area.
• WAEC 2025 · Paper 1 · Q32A sector has angle $108^\circ$ and radius $3\frac12\text{ cm}$. Find its perimeter. $\left[\pi = \frac{22}{7}\right]$
• NECO 2024 · Paper 1 · Q36Calculate the area of trapezium $ABCD$ in the diagram, where $AB \parallel DC$, $|AB| = 8\text{ cm}$, $|DC| = 16\text{ cm}$, $|BC| = 12\text{ cm}$ …
• NECO 2024 · Paper 1 · Q40Calculate the length of an arc which subtends an angle of $66^\circ$ at the centre of a circle of radius $8\text{ cm}$, correct to one decimal …
• WAEC 2024 · Paper 1 · Q20A piece of rod of length $44\text{ m}$ is cut to form a rectangular shape such that the ratio of the length to the breadth is $7 : 4$. Find the …
• WAEC 2024 · Paper 1 · Q33Find, correct to the nearest whole number, the value of $h$ in the diagram.
• WAEC 2024 · Paper 1 · Q36The perimeter of a rectangular garden is $90\text{ m}$. If the width is $7\text{ m}$ less than the length, find the length of the garden.
• WAEC 2024 · Paper 1 · Q41Two opposite sides of a rectangle are $(5x + 3)\text{ m}$ and $(2x + 9)\text{ m}$. If an adjacent side is $(6x - 7)\text{ m}$, find, in $\text{m}^2$, …
• WAEC 2024 · Paper 1 · Q43The area of a sector of a circle with radius $7\text{ cm}$ is $51.3\text{ cm}^2$. Calculate, correct to the nearest whole number, the angle …
• NECO 2023 · Paper 1 · Q15The area of a rectangular piece of cardboard is $104\text{ cm}^2$. If its width is $8\text{ cm}$, find its perimeter.
• WAEC 2023 · Paper 1 · Q27The length of the diagonal of a square is $12\text{ cm}$. Calculate the area of the square.
• WAEC 2023 · Paper 1 · Q33The angle of a sector of a circle of radius $3.4\text{ cm}$ is $115^\circ$. Find the area of the sector. $\left[\text{Take }\pi = \frac{22}{7}\right]$
• WAEC 2023 · Paper 1 · Q34The diagonals of a rhombus are $16\text{ cm}$ and $12\text{ cm}$. Find the length of a side.
• NECO 2022 · Paper 1 · Q26The perimeter of a rectangle is 44 m and its area is $120\text{ m}^2$. Find the dimensions of the rectangle.
• NECO 2022 · Paper 1 · Q40A sector of a circle subtends an angle of $90^\circ$ at the centre of the circle. If the area of the sector is $11\text{ cm}^2$, find its radius …
• NECO 2022 · Paper 1 · Q59When a stone is dropped into water, the radius of a circular wave is increasing at the rate of $0.2\text{ m s}^{-1}$. Find the rate at which …
• NECO 2022 · Paper 1 · Q9A toy train starts at the station and moves around a circular track of 220 cm. How many rotations will it move along the track when it has covered …
• WAEC 2022 · Paper 1 · Q21In the diagram, $\angle POQ = 150^\circ$ and the radius of the circle $PSQR$ is $4.2\text{ cm}$. Find the length of the minor arc $PRQ$. $\left[\text{Take }\pi = \frac{22}{7}\right]$
• WAEC 2022 · Paper 1 · Q22In the diagram, $\angle POQ = 150^\circ$ and the radius of the circle $PSQR$ is $4.2\text{ cm}$. Find the area of the sector $OPSQ$. $\left[\text{Take }\pi = \frac{22}{7}\right]$
• WAEC 2022 · Paper 1 · Q25In the diagram, $\angle WZY$ and $\angle WYX$ are right angles. Find the perimeter of $WXYZ$.
• WAEC 2022 · Paper 1 · Q26The length of a rectangle is $10\text{ cm}$. If its perimeter is $28\text{ cm}$, find the area.
• WAEC 2022 · Paper 1 · Q41The lengths of the parallel sides of a trapezium are $9\text{ cm}$ and $12\text{ cm}$. If the area of the trapezium is $105\text{ cm}^2$, find …
• WAEC 2022 · Paper 1 · Q44A rectangle has width $\frac34\text{ cm}$ and area $3\frac38\text{ cm}^2$. Find the length of the rectangle.
• WAEC 2021 · Paper 1 · Q11The circumference of a circular track is $9\text{ km}$. A cyclist rides round it a number of times and stops after covering a distance of $302\text{ km}$. …
• WAEC 2021 · Paper 1 · Q24The diagonals of a rhombus are $12\text{ cm}$ and $5\text{ cm}$. Calculate its perimeter.
• WAEC 2021 · Paper 1 · Q30A trapezium with parallel sides $10\text{ cm}$ and $21\text{ cm}$ and height $8\text{ cm}$ is inscribed in a circle of radius $7\text{ cm}$. …
• WAEC 2020 · Paper 1 · Q31The length of an arc of a circle of radius $3.5\text{ cm}$ is $1\frac{19}{36}\text{ cm}$. Calculate, correct to the nearest degree, the angle …
• WAEC 2020 · Paper 1 · Q32In the diagram, $PU \parallel SR$, $PS \parallel TR$, $QS \parallel UR$, $|UR| = 15\text{ cm}$, $|SR| = 8\text{ cm}$, $|PS| = 10\text{ cm}$ and …
• WAEC 2019 · Paper 1 · Q25An arc subtends an angle of $72^\circ$ at the centre of a circle. Find the length of the arc if the radius of the circle is $3.5\text{ cm}$. …
• WAEC 2019 · Paper 1 · Q28Find the angle which an arc of length $22\text{ cm}$ subtends at the centre of a circle of radius $15\text{ cm}$. $\left[\text{Take }\pi = \frac{22}{7}\right]$
• WAEC 2019 · Paper 1 · Q29A rectangular board has a length of $15\text{ cm}$ and width $x\text{ cm}$. If its sides are doubled, find its new area.
• WAEC 2019 · Paper 1 · Q38In the diagram, $O$ is the centre of the circle of radius $18\text{ cm}$. If $\angle ZXY = 70^\circ$, calculate the length of arc $ZY$. $\left[\text{Take }\pi = \frac{22}{7}\right]$
• JAMB 2017 · UTME · Q12$PQRSTV$ is a regular hexagon of side $7\text{ cm}$ inscribed in a circle. Find the circumference of the circle. $\left[\text{Take }\pi = \frac{22}{7}\right]$
• JAMB 2017 · UTME · Q30A circle of perimeter $28\text{ cm}$ is opened to form a square. What is the maximum possible area of the square?
• JAMB 2016 · UTME · Q30In the figure, $PQST$ is a parallelogram and $TSR$ is a straight line. If the area of $\triangle QRS$ is $20\text{ cm}^2$, find the area of the …
• JAMB 2015 · UTME · Q16In the figure, $PQ \parallel SR$, $ST \parallel RQ$, $PS = 7\text{ cm}$, $PT = 7\text{ cm}$ and $SR = 4\text{ cm}$. Find the ratio of the area …
• JAMB 2015 · UTME · Q22A sector of a circle is bounded by two radii $7\text{ cm}$ long and an arc of length $6\text{ cm}$. Find the area of the sector.
• JAMB 2015 · UTME · Q31An arc of a circle subtends an angle of $70^\circ$ at the centre. If the radius of the circle is $6\text{ cm}$, calculate the area of the sector. …
• JAMB 2013 · UTME · Q27A square tile has side $30\text{ cm}$. How many of these tiles will cover a rectangular floor of length $7.2\text{ m}$ and width $4.2\text{ m}$?
• JAMB 2013 · UTME · Q29A chord of a circle subtends an angle of $120^\circ$ at the centre of a circle of diameter $4\sqrt3\text{ cm}$. Calculate the area of the major …
• JAMB 2012 · UTME · Q28Find the area of the trapezium $PQRS$, where $PQ = 7\text{ cm}$, $SR = 13\text{ cm}$ and the height $PS = 6\text{ cm}$.
• JAMB 2012 · UTME · Q29A circular arc subtends an angle of $150^\circ$ at the centre of a circle of radius $12\text{ cm}$. Calculate the area of the sector.
• JAMB 2011 · UTME · Q28A circle of perimeter $28\text{ cm}$ is opened to form a square. What is the maximum possible area of the square?
• JAMB 2010 · UTME · Q31If the two smaller sides of a right-angled triangle are $4\text{ cm}$ and $5\text{ cm}$, find its area.
• JAMB 2010 · UTME · Q32An arc subtends an angle of $50^\circ$ at the centre of a circle of radius $6\text{ cm}$. Calculate the area of the sector formed. $\left[\text{Take }\pi = \frac{22}{7}\right]$
• JAMB 2010 · UTME · Q39If the area of $\triangle PQR$ is $12\sqrt3\text{ cm}^2$, $|PQ| = 8\text{ cm}$, $|PR| = q$ and $\angle QPR = 60^\circ$, find the value of $q$.
• JAMB 2004 · UME · Q25$PQRSTV$ is a regular polygon of side 7 cm inscribed in a circle. Find the circumference of the circle $PQRSTV$. $\left[\pi = \frac{22}{7}\right]$
• JAMB 2004 · UME · Q27In the diagram, $PQ = 4$ cm and $TS = 6$ cm; $PQTU$ and $PQRS$ are parallelograms. If the area of parallelogram $PQTU$ is $32\text{ cm}^2$, find …
• JAMB 2004 · UME · Q28An arc of a circle of length 22 cm subtends an angle of $3x^\circ$ at the centre of the circle. Find the value of $x$ if the diameter of the …
• JAMB 2003 · UME · Q32An arc of a circle subtends an angle of $30^\circ$ at the circumference of a circle of radius 21 cm. Find the length of the arc. $\left[\pi = \frac{22}{7}\right]$
• JAMB 2003 · UME · Q33A trapezium has two parallel sides of length 5 cm and 9 cm. If the area is $21\text{ cm}^2$, find the distance between the parallel sides.
• JAMB 2003 · UME · Q34$XYZ$ is a circle with centre $O$ and radius 7 cm, and $\angle XZY = 45^\circ$. Find the area of the shaded segment cut off by $XY$. $\left[\pi = \frac{22}{7}\right]$
• JAMB 2002 · UME · Q10In the diagram, $XZ$ is the diameter of the circle $XYZ$ with centre $O$ and radius $\frac{15}{2}$ cm. If $XY = 12$ cm, find the area of the …
• JAMB 2002 · UME · Q12A chord of a circle subtends an angle of $120^\circ$ at the centre of a circle of diameter $4\sqrt3$ cm. Calculate the area of the major sector.
• JAMB 2002 · UME · Q7In the diagram are two concentric circles of radii $r$ and $R$ with centre $O$. If $r = \frac25R$, express the area of the shaded ring in terms …
• JAMB 2001 · UME · Q25The chord $ST$ of a circle is equal to the radius $r$ of the circle. Find the length of the arc $ST$.
• JAMB 2000 · UME · Q27An equilateral triangle of side $\sqrt3$ cm is inscribed in a circle. Find the radius of the circle.
• JAMB 1998 · UME · Q27In the figure, $PQST$ is a parallelogram and $TSR$ is a straight line, with $TS = 10$ cm and $SR = 8$ cm. If the area of $\triangle QRS$ is $20\text{ cm}^2$, …
• JAMB 1998 · UME · Q31The locus of all points at a distance 8 cm from a point $N$ passes through points $T$ and $S$. If $S$ is equidistant from $T$ and $N$, find the …
• JAMB 1997 · UME · Q28A chord of a circle of diameter 42 cm subtends an angle of $60^\circ$ at the centre. Find the length of the minor arc. $\left[\pi = \frac{22}{7}\right]$
• JAMB 1997 · UME · Q29An arc of a circle subtends an angle of $70^\circ$ at the centre. If the radius of the circle is 6 cm, calculate the area of the sector. $\left[\pi = \frac{22}{7}\right]$
• JAMB 1995 · UME · Q34In the diagram, $PR = 10$ cm and $\angle QPR = 30^\circ$. Find $PQ$ if the area of triangle $PQR$ is $35\text{ cm}^2$.
• JAMB 1994 · UME · Q30Calculate the perimeter, in cm, of a sector of a circle of radius 8 cm and angle $45^\circ$.
• JAMB 1994 · UME · Q32A triangle has base 7 cm and other sides 6 cm and 5 cm. Find its height $h$ onto the base.
• JAMB 1993 · UME · Q27Calculate the length, in cm, of the arc of a circle of diameter 8 cm which subtends an angle of $22\frac12^\circ$ at the centre.
• JAMB 1993 · UME · Q35In the figure, the area of the square $PQRS$ is $100\text{ cm}^2$. If the ratio of the area of the square $TUYS$ to the area of the square $XQVU$ …
• JAMB 1993 · UME · Q37Find the area of the sector of a circle with radius 3 m if the angle of the sector is $60^\circ$.
• JAMB 1992 · UME · Q2The radius of a circle is given as 5 cm subject to an error of 0.1 cm. What is the percentage error in the area of the circle?
• JAMB 1992 · UME · Q30The diagram shows a circle with centre $O$ and radius 6 cm; two radii are at right angles. Find the area of the shaded segment.
• JAMB 1991 · UME · Q32The area of a square is $144\text{ cm}^2$. Find the length of its diagonal.
• JAMB 1991 · UME · Q44In the figure, $PQRS$ is a square of side 8 cm; $UQ = 4$ cm, $QV = 6$ cm and $WR = 2$ cm. What is the area of $\triangle UVW$?
• JAMB 1990 · UME · Q23The perimeter of a rectangular lawn is 24 m. If the area of the lawn is $35\text{ m}^2$, how wide is the lawn?
• JAMB 1990 · UME · Q31In a trapezium $PQRS$ with $QR \parallel PS$, the area is $73.5\text{ cm}^2$ and the height is 10.5 cm. Find the length of $PS$ if $QR$ is one-third …
• JAMB 1990 · UME · Q32The angle of a sector of a circle of radius 10.5 cm is $48^\circ$. Calculate the perimeter of the sector. $\left[\pi = \frac{22}{7}\right]$
• JAMB 1990 · UME · Q41In the figure, $PQR$ is a semicircle on $PR$, below the rectangle $OPRS$ with $OP = 11$ cm. The triangle $OTS$, with $OT = 6$ cm, $TS = 8$ cm …
• JAMB 1989 · UME · Q43A square tile has side 30 cm. How many of these tiles cover a rectangular floor of length 7.2 m and width 4.2 m?
• JAMB 1988 · UME · Q33In the figure, $PS = 7$ cm and $RY = 9$ cm. If the area of parallelogram $PQRS$ is $56\text{ cm}^2$, find the area of trapezium $PQTS$.
• JAMB 1988 · UME · Q34A quadrant of a circle of radius 6 cm is cut away from each corner of a rectangle 25 cm long and 18 cm wide. Find the perimeter of the remaining …
• JAMB 1987 · UME · Q3A rectangular lawn has an area of 1815 square yards. If its length is 50 metres, find its width in metres, given that 1 metre equals 1.1 yards.
• JAMB 1987 · UME · Q37In the figure, $PQRS$ is a rectangle $2h$ cm wide and $3h$ cm high. The shaded U-shaped region is made of 2 cm strips along the two vertical …
• JAMB 1987 · UME · Q6If the length of a square is increased by $20\%$ while its width is decreased by $20\%$ to form a rectangle, what is the ratio of the area of …
• JAMB 1986 · UME · Q38An arc of a circle of radius 6 cm is 8 cm long. Find the area of the sector.
• JAMB 1985 · UME · Q33In $\triangle XYZ$, $\angle XKZ = 90^\circ$, $XK = 15$ cm, $XZ = 25$ cm and $YK = 8$ cm. Find the area of $\triangle XYZ$.
• JAMB 1985 · UME · Q36Find the area of a regular hexagon inscribed in a circle of radius 8 cm.
• JAMB 1985 · UME · Q42$PQRS$ is a trapezium of area $14\text{ cm}^2$ in which $PQ \parallel RS$. If $PQ = 4$ cm and $SR = 3$ cm, find the area of $\triangle SQR$ in …
• JAMB 1985 · UME · Q47In the figure, a sector of a circle of radius 3 has an angle of $120^\circ$ at the centre. The area of the shaded segment is
• JAMB 1983 · UME · Q39A square of side 0.524375 cm is drawn on a square paper of side 2.524375 cm. Find the area of the paper not covered by the drawing, correct to …
• JAMB 1983 · UME · Q45$PQR$ is the diameter of a semicircle $RSP$ with centre $Q$ and radius 3.5 cm. If $\angle QPT = \angle QRT = 60^\circ$, find the perimeter of …