In 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 sides and along the top. If the shaded area is 72 cm2, find h.
Worked solution (try it first)
The two side strips run the full height: each is 2×3h, so together they are 12h cm2.
The top strip fits between them, so its length is 2h−4: its area is 2(2h−4)=4h−8.
Shaded area: 12h+4h−8=72, so 16h=80 and h=5 cm, option D.