Question

In a four-sided 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

Given:

Longer diagonal AC = 128 m.

Perpendiculars from the opposite vertices to AC are 22.7 m and 17.3 m.

Step-wise calculation:

1. The diagonal divides the quadrilateral into two triangles.

So Area = Area(Δ on one side) + Area(Δ on the other side).

= `1/2 xx AC xx 22.7 + 1/2 xx AC xx 17.3` which combines to Area = `1/2 xx AC xx (22.7 + 17.3)`.

2. Substitute values:

Area = `1/2 xx 128 xx (22.7 + 17.3)`

= 64 × 40.0

= 2560 m²

Area of the field = 2560 m².