Question

Find the area of a quadrilateral, the length of one of its diagonals being 80 m and the lengths of the perpendiculars upon it from the opposite corners are 16 m and 24 m.

Answer 1

Given: One diagonal = 80 m; perpendiculars from the opposite corners to that diagonal = 16 m and 24 m.

Step-wise calculation: 

The diagonal splits the quadrilateral into two triangles.

So, area = `1/2` × diagonal × sum of the two perpendiculars. 

So, area = `1/2 xx 80 xx (16 + 24)`

= 40 × 40

= 1600 m²

The area of the quadrilateral is 1600 m².