Area and Perimeter Practice Test 1

For ΔBCF
s = $\frac{21+17+10}{2}$ = 24 m
Area of Δ BCF = $\sqrt{24\left(24-21\right)\left(24-17\right)\left(24-10\right)}$
= $\sqrt{24\times 3\times 7\times 14}$
= $\sqrt{2\times 2\times 2\times 3\times 3\times 7\times 2\times 7}$
= 2 × 2 × 3 × 7 = 84 ${\mathit{m}}^2$
Now, $\frac{1}{2}$ × 21 × CE = 84
∴ CE = $\frac{84\times 2}{21}$ = 8 m
Hence, Area of trapezium ABCD = $\frac{1}{2}\left(41+20\right)\times 8$
= 61 × 4 = 244 ${\mathit{m}}^2$
Total cost of levelling = 244 × Rs. 30 = Rs. 7320