Question

In the given figure, find the area of the parallelogram ABCD if the area of shaded triangle is 9 cm${}^2$. [4 marks]

Answer 1

Area of a parallelogram = Base $\times$ Height [0.5 mark]

Base of the parallelogram ABCD = BC
= BE + EC
= 3 + 4 = 7 cm
[0.5 mark]

We need to find the height AE now, in order to find the area of the parallelogram ABCD. [0.5 mark]

We are given area of triangle ABE = 9 cm${}^2$
Area of a triangle = $\frac{1}{2}\times$ Base $\times$ Height [0.5 mark]
Given that area = 9 cm${}^2$ and base, BE = 3 cm
So, 9 = $\frac{1}{2}\times$ BE $\times$ AE
Or, 9 = $\frac{1}{2}\times$ 3 $\times$ AE
AE = $\frac{9\times 2}{3}$ = 6 cm [1 mark]

So, area of parallelogram ABCD = Base $\times$ Height
= BC $\times$ AE
= 7 $\times$ 6
= 42 cm${}^2$ [1 mark]