□PQRS is the map of a plot of land. Using the given measures, find its area.

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Solution

The given map of the plot is of a quadrilateral that can be divided into three triangles
∆QPS, ∆STQ, ∆STR
All the three triangles are right triangles.
Area of a right triangle = $\frac{1}{2}$ (Base × Height)
Total area of the plot = A (∆QPS) + A (∆STQ) + A (∆STR)
A (∆PQS) = $\frac{1}{2} \times 9 \times 40$ = 180 sq m
A (∆STR) + A (∆QST) = $\frac{1}{2} \times 13 \times 60$ = 390 sq m
Total area = 390 sq m + 180 sq m = 570 sq m
∴ The area of the plot is 570 sq m

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