Mensuration Practice Test 6

Sides of triangle ABC
a = 14, b = 13, c = 15
s = $\frac{\mathit{a}+\mathit{b}+\mathit{c}}{2}$ = $\frac{14+13+15}{2}$ = $\frac{42}{2}$ = 21
Area of triangle ABC = $\sqrt{\mathit{s}\left(\mathit{s}-\mathit{a}\right)\left(\mathit{s}-\mathit{b}\right)\left(\mathit{s}-\mathit{c}\right)}$
= $\sqrt{2\left(21-14\right)\left(21-13\right)\left(21-15\right)}$
= $\sqrt{21\times 7\times 8\times 6}$
= $\sqrt{3\times 7\times 7\times 2\times 2\times 2\times 2\times 3}$
= 2 × 2 × 3 × 7 = 84 sq. m
Area of the parallelogram = 2 × 84 = 168 sq. m