Question

In a four-sides field, the length of the longer diagonal is 128 m. The lengths of perpendiculars from the opposite vertices upon this diagonal are 22.7 m and 17.3 m. Find the area of the field.

Answer 1

The field, which is represented as ABCD, is given below.

The area of the field is the sum of the areas of triangles ABC and ADC.

Area of the triangle ABC$=\frac{1}{2}\left(\mathrm{AC}\times \mathrm{BF}\right)=\frac{1}{2}\left(128\times 22.7\right)=1452.8{\mathrm{m}}^2$

Area of the triangle ADC$=\frac{1}{2}\left(\mathrm{AC}\times \mathrm{DE}\right)=\frac{1}{2}\left(128\times 17.3\right)=1107.2{\mathrm{m}}^2$

Area of the field = Sum of the areas of both the triangles$=1452.8+1107.2=2560{\mathrm{m}}^2$