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Chapter 11: Q19. (page 431)

Find the area of each figure:

A square inscribed in a circle with radiusr.

Short Answer

Expert verified

The area of given figure is 2r2square units.

Step by step solution

01

Step 1. Analyze the given information.

Let the side of the square is x and the radius of circle r ,

Then, DB=r+r=2r

02

Step 2. Concept Used.

We can use Pythagoras theorem.

Pythagorean Theorem define that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

In鈻�BCD

DB2=BC2+CD2

(2r)2=x2+x2

2x2=4r2

x2=2r2

x=2r

Thus, the side of square is2r

03

Step 3. Find the area of given figure.

Area of square can be found using the formula

A=s2

Where,

s= Side of square

A=(2r)2

=2r2Square units.

Therefore, the area of given figure is 2r2square units.

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