A farmland is in the shape of a rhombus. The perimeter of the land is 100 m and the length of one of the diagonals is 40 m. The land is divided into four equal parts. What is the area of each part?

Explanation

Perimeter = 100 m implies side = 25 m. The diagonals of a rhombus bisect each other at 90^\circ. One half-diagonal is 20 m. By Pythagoras, the other half-diagonal is \sqrt{25^2 - 20^2} = \sqrt{225} = 15 m. The four equal parts are right triangles formed by the diagonals. Area of one such part = \frac{1}{2} \times 20 \times 15 = 150 square metres.

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