Question : The diagonal of a quadrilateral-shaped field is 24 m and the perpendiculars dropped on it from the remaining opposite vertices are 8 m and 13 m. The area of the field is:
Option 1: 252 m2
Option 2: 156 m2
Option 3: 96 m2
Option 4: 1152 m2
Correct Answer: 252 m 2
Solution :
Given, the length of the diagonal, $d$ = 24 m
Heights of perpendicular, $h_1$ and $h_2$, are 8 m and 13 m
Area of given quadrilateral = $\frac{1}{2}\times d\times h_1+\frac{1}{2}\times d\times h_2$
= $\frac{1}{2}\times 24\times (8+13)$
= 252 m
2
Hence, the correct answer is 252 m
2
.
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