Question

7. 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

Step-by-step explanation:

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:

42 cm²

Step-by-step explanation:

I have attached the answer. Here I will give you the explanation!

First is entry the given values under appropriate headings, so it will be easy for you.

Next the value of radius is not given, but the question says that the side of square is equal to 14 cm & they gave the circles touch externally on the side of square. So the value of radius is 7cm.

Then they asked the area of shaded one.

So you need to subtract the area of quadrant from the area of square.

And you need to substitute the values given in the beginning down.

If the question gives you the value of pi then use it, otherwise you 22/7

Then calculate as given in the attachment you will get the answer as 42 cm².

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