Q6 of 27 Page 228

In adjacent figure A, B, C and D are centers of equal circles which touch externally in pairs and ABCD is a square of side 7 cm. Find the area of the shaded region.

Side of square, a = 7cm


Area of square, AS = a2


⇒ AS = 72 = 49 sq.cm



⇒ R = 3.5 cm



There is a quadrant of each of four circles that is present inside the square,




⇒ AQ = 9.625 sq.cm


Shaded area = Area(square) – [4 × area(quadrant)]


⇒ Shaded area = AS – [4 × AQ]


⇒ 49 – (4 × 9.625)


⇒ 49 – 38.5


⇒ 10.5 sq.cm


∴ Area of shaded region is 10.5 sq.cm


More from this chapter

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4

The adjacent figure consists of four small semi-circles of equal radii and two big semi-circles of equal radii (each 42 cm). Find the area of the shaded region.

 5

The adjacent figure consists of four half circles and two quarter circles. If OA = OB = OC = OD = 14 cm. Find the area of the shaded region.

 7

The area of an equilateral triangle is 49√3 cm2. Taking each angular point as centre, a circle is described with radius equal to half the length of the side of the triangle as shown in the figure. Find the area of the portion in the triangle not included in the circles.

 8

Four equal circles, each of radius ‘a’ touch one another. Find the area between them.