A field is a trapezium whose parallel sides are 25 m and 11 m. Its two non-parallel sides are 13 m and 15 m. What is the area of the field?

Explanation

1. 01

   Cut off a parallelogram of sides 11 m and 13 m. What remains is a triangle with sides 13 m, 15 m and $25 - 11 = 14$ m, with the same height as the trapezium.

2. 02

   That triangle has $s = 21$, so area = $\sqrt{21 \times 8 \times 6 \times 7} = 84$ m².

3. 03

   Height = $2 \times 84 \div 14 = 12$ m.

4. 04

   Trapezium area = $\frac{1}{2} \times (25 + 11) \times 12 = 216$ m².