Question

The area of the circle is 220 cm square. The area of the square inscribed in it is -

Answer 1

Step-by-step explanation:

Here, we have the area of circle

Area of circle = 220cm

we know the formula for area of circle,

Area of circle = π r²

220 = (22/ 7) x r²

( 220 X 7) /22= r²

√ ((10 x 7 )) = r

√70 = r

Now,

Diagonal of the inscribed square

= diameter of circle

Diagonal of the square

= 2 radius

= 2 (√70 ) cm

we know,

Area of square = (side) x (side)

side of square = diagonal /√2

= (2 √70 ) /√2

= ((√2 x √2 )√70 ) /√2

= √70 x √2

= √ 140 cm

therefor,

Area of square = ( √140) (√140)

= 140 cm²

The area of the square inscribed in a given circle is 140cm²

Answer 2

Answer: 140 cm²

Step-by-step explanation:

Given : The area of circle is 220 cm²

To find : The area of square whose vertices are on the circle?

Solution :

Area of the circle = 220 cm.sq.

πr² = 220

r² = 70

» r = √70

We know that :

The radius of the circle is half the diagonal of the square.

Diagonal of square = 2√70

By Pythagoras theorem,

a² + a² = (2√70)²

2a² = 4 × 70

a² = 140

a = √140

Side of the square = (√140)

Area of the square = (Side)²

= (√140)²

= 140 cm²

Area of the square is 140 cm²

Therefore, Area of the square = 140 cm².