Mensuration Practice Test 6

In a parallelogram, opposite sides are equal.
5b = 4a
These are not co-prime numbers. The value of b must be 4 and value of a must be 5.
Area of Parallelogram = b × h = 120
5b × 3c = 120
bc = $\frac{120}{15}$ = 8

Area of triangle ABX = $\frac{1}{2}\times 3\mathit{b}\times 3\mathit{c}$
= $\frac{9\mathit{b}\mathit{c}}{2}$ = $\frac{9\times 8}{2}$
= 36 $\mathit{c}{\mathit{m}}^2$
Now bc = 8
c = $\frac{8}{\mathit{b}}$ = $\frac{8}{4}$ = 2 cm.
Area of triangle ZDY = $\frac{1}{2}\times \mathit{a}\times \mathit{c}$
= $\frac{1}{2}\times 5\times 2$ = $\frac{10}{2}$ = 5
Area of pentagon AXCYZ = 120 − (36 + 5)
= 120 − 41
= 79 $\mathit{c}{\mathit{m}}^2$