Q1 of 52 Page 159

In figure 7.43, A is the centre of the circle. ∠ ABC = 45° and AC = 7√2 cm. Find the area of segment BXC.

From the property we know that, If two sides of a triangle are equal then their corresponding angles are also equal.


So, as AB = AC,


⇒ ∠ ABC = ∠ ACB = 45°


As the sum of angles of triangle is equal o 180°


⇒ ∠ BAC = 90°




⇒ AT = 49 sq.cm


Area of sector (A – BXC), AS = one-fourth of circle




⇒ AS = 77 sq.cm


Area of shaded region, AR = AS - AT


⇒ AR = 77 – 49


⇒ AR = 28 sq.cm


∴ The area of the shaded region is 28 sq. cm


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12

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.

 13

∆ LMN is an equilateral triangle. LM = 14 cm. As shown in figure, three sectors are drawn with vertices as centre and radius7 cm. Find,


(1) A (Δ LMN)


(2) Area of any one of the sectors


(3) Total area of all three sectors


(4) Area of shaded region

 2

In the figure 7.44, O is the centre of the circle. M (arc PQR) = 60° OP = 10 cm.

Find the area of the shaded region. (π = 3.14, √3 = 1.73)


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In the figure 7.45, if A is the centre of the circle. ∠ PAR = 30°, AP = 7.5, find the area of the segment PQR. (π = 3.14)