Q12 of 52 Page 154

In figure 7.35, □PQRS is a rectangle. If PQ = 14 cm, QR = 21 cm, find the areas of the parts x, y and z.

Since part x is a sector of a circle with radius, r = 14 cm and the central angle is 90°, so the area of x will be equal to one-fourth of the area of circle with PQ as radius.


Area of circle with PQ as radius = π (PQ)2




⇒ x = 154 sq. cm


Similarly, area y is also equal to one-fourth od area of circle with radius, r = QR – PQ


⇒ r = 21 – 14 = 7 cm


Area of circle with r as radius = π (r)2




⇒ y = 38.5 sq. cm


Also,


z = Area of rectangle(PQRS) – x – y


Area of rectangle = PQ× QR


⇒ Area of rectangle = 14× 21 = 294 sq. cm


⇒ z = 294 – 154 – 38.5


⇒ z = 101.5 sq.cm


∴ the area of x, y and z are 154 sq.cm, 38.5 sq.cm and 101.5 sq.cm respectively


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