Flashcards · 12 cards

Plane mensuration

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Rule
The area of a parallelogram?
Answer
Base × perpendicular height: $A = bh$ . Not base × slant side.
From the lesson: Areas of flat shapes
Rule
The area of a triangle?
Answer
$A = \frac12 bh$ , with the height at right angles to the base.
From the lesson: Areas of flat shapes
Rule
The area of a trapezium?
Answer
$A = \frac12(a + b)h$ : half the sum of the parallel sides, times the distance between them.
From the lesson: Areas of flat shapes
Rule
The area of a rhombus from its diagonals?
Answer
$A = \frac12 d_1 d_2$ .
From the lesson: Areas of flat shapes
Rule
The area of a triangle from two sides and the angle between them?
Answer
$A = \frac12 ab\sin C$ .
From the lesson: Areas of flat shapes
Rule
The circumference and area of a circle?
Answer
$C = 2\pi r$ (or $\pi d$ ) and $A = \pi r^2$ . Check whether you were given the radius or the diameter.
From the lesson: Circles, arcs and sectors
Rule
The arc length and area of a sector with angle $\theta$ ?
Answer
Arc $= \dfrac{\theta}{360} \times 2\pi r$ and area $= \dfrac{\theta}{360} \times \pi r^2$ : a fraction of the whole circle.
From the lesson: Circles, arcs and sectors
Know it
The perimeter of a sector?
Answer
Arc $+ \ 2r$ : all the way round, including both radii.
From the lesson: Circles, arcs and sectors
Rule
The area of a segment?
Answer
Sector minus triangle: $\dfrac{\theta}{360}\pi r^2 - \dfrac12 r^2\sin\theta$ .
From the lesson: Segments, chords and composite shapes
Rule
The length of a chord that makes an angle $\theta$ at the centre?
Answer
$2r\sin\dfrac{\theta}{2}$ : the perpendicular from the centre halves both the chord and the angle.
From the lesson: Segments, chords and composite shapes
Know it
The perimeter of a segment?
Answer
Arc + chord. The radii are inside the segment, so they don't count.
From the lesson: Segments, chords and composite shapes
Which method?
WAEC 2022 · Paper 2 · Q3
A 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. $\left[\text{Take }\pi = \frac{22}{7}\right]$
Perimeter (m, 1 d.p.)
What makes up the perimeter?
Answer
A segment's perimeter is its arc plus its chord. Half the chord is $24.5\sin 36^\circ$ ; the arc is $\frac{72}{360} \times 2\pi r$ .
From the lesson: Segments, chords and composite shapes Try the question