Question

In Fig. 12.25, ABCD is a square of side 14 cm. With
centres A, B, C and D, four circles are drawn such
that each circle touch externally two of the remaining
three circles. Find the area of the shaded region.​

Answer 1

Answer:

Area of shaded region

Given: Side of square ABCD = 14 cm

Radius of circles with centers A, B, C and D = 14/2 = 7 cm

Area of shaded region = Area of square - Area of four sectors subtending right angle

Area of each of the 4 sectors is equal to each other and is a sector of 90° in a circle of 7 cm radius. So, Area of four sectors will be equal to Area of one complete circle

So

Area of 4 sectors = Πr²

Area of square ABCD = (Side)²

Area of square ABCD = (14)²

Area of square ABCD = 196 cm²

Area of shaded portion = Area of square ABCD - 4 × Area of each sector

= 196 – 154

= 42 cm²

Therefore, the area of shaded portion is 42 cm²

Answer 2

Answer:

=(196-154) cm2=42cm2.

Step By Step:

Now area of shaded  portion =Area of square, ABCD -The sum of the areas of four quadrants at the four corners of the square =(196-154) cm2=42cm2.