Given: In rectangle PQRS,
PQ = 14 cm, QR = 21 cm
To find: Areas of the parts x, y and z.
∠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 \(\Box\)PQRS = PQ × QR
= 14 × 21 = 294 cm2
Area of part z = area of \(\Box\)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.