Question

Question 4
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. Find the area of the field.

Answer 1

Here, $h_1=13m,h_2=8andAC=b=24m$
Area of quadrilateral ABCD = Area of $\Delta$ ABC + Area of $\Delta$ ADC

= $\frac{1}{2}b\times h_1+\frac{1}{2}b\times h_1$
= $\frac{1}{2}b(h_1+h_2)$
= $\frac{1}{2}\times 24\times (13+8)=\frac{1}{2}\times 24\times 21=252m^2$
Hence required area of the field is $252m^2$