Question

Four equal circles are described about four corners of a square so that each touches the two of others. Find the area of a part pf a square enclosed by the circles if the side of the square is 14 cm

Answer 1

Dear User!

Question:

Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces. Find the area of the portion enclosed between these pieces.

Method of Solution:

Given: Four circular cardboard pieces of radii 7 cm are placed on a paper in such a way that each piece touches other two pieces.

Now,

Area of Square (ABCD) = Side × Side

Area of Square (ABCD) = 14×14 cm²


Area of Square (ABCD) =196m²

Now, There are four Quadrant in a Square which are given in attachment!

Area of 4 Quadrant = (4×1/4×πr²)

Area of 4 Quadrant =22×7 cm²

Area of 4 Quadrant = 154cm²

Therefore, Area of portion= of Square (ABCD) - Area of 4 Square



Area of portion= 196-154 cm²

Area of portion = 42 cm²


Hence, Required Area of portion enclosed between these pieces are 42cm².

Answer 2

here is your answer OK ☺☺☺☺☺


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.


area of each sector =
$\frac{90}{360} \times ({7}^{2} )$

= 1/4 x 22/7 x 7 x 7

= 77/2 cm'2

Area of square ABCD = (Side)2 = (14)2 = 196 cm2

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

196-4 x 77/2 = 196 - 154


42 answer OK ☺☺☺☺


Therefore, the area of shaded portion is 42 cm2.