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

Given: In rectangle PQRS, 

PQ = 14 cm, QR = 21 cm 

To find: Areas of the parts x, y and z.

1 Answer

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∠Q = ∠R = θ = 90° …[Angles of a rectangle]

For the sector (Q – PA),

PQ = QA …[Radii of the same circle]

∴ QA = 14 cm 

Now, QR = QA + AR … [Q – A – R] 

∴ 21 = 14 + AR 

∴ AR = 7 cm

Area of rectangle = length × breadth 

area of PQRS = PQ × QR 

= 14 × 21 

= 294 cm2 

Area of part z = area of PQRS

– area of part x – area of part y 

= 294 – 154 – 38.5 

= 101.5 cm2 

∴ The area of part x is 154 cm2, the area of part y is 38.5 cm2 and the area of part z is 101.5 cm2.

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