Question

In the given figure,$\square$ PQRS is a rectangle. If PQ = 14 cm, QR = 21 cm, find the areas of the parts x, y and z .

Answer 1

PQRS is a rectangle.

∴ ∠Q = ∠R = 90º

Radius of sector PTQ = PQ = 14 cm

∴ Area of part x = Area of the sector PTQ = $\frac{\theta }{360°}\times \mathrm{\pi }{r}^2=\frac{\angle \mathrm{Q}}{360°}\times \mathrm{\pi }\times {\left(\mathrm{PQ}\right)}^2=\frac{90°}{360°}\times \frac{22}{7}\times {\left(14\right)}^2$ = 154 cm²

Radius of sector TUR = TR = QR − QT = QR − PQ = 21 − 14 = 7 cm (QT = PQ)

∴ Area of part y = Area of the sector TUR = $\frac{\theta }{360°}\times \mathrm{\pi }{r}^2=\frac{\angle \mathrm{R}}{360°}\times \mathrm{\pi }\times {\left(\mathrm{TR}\right)}^2=\frac{90°}{360°}\times \frac{22}{7}\times {\left(7\right)}^2$ = 38.5 cm²

Now,

Area of rectangle PQRS = QR × PQ = 21 × 14 = 294 cm²

∴ Area of part z = Area of rectangle PQRS − Area of part x − Area of part y = 294 − 154 − 38.5 = 101.5 cm²