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