A circle is inscribed in a square. If the length of the diagonal of the square is 14
2
cm, what is the area of the circle?
- A308 sq cm
- B462 sq cm
- C154 sq cm
- D616 sq cm
Solution & Step-by-step Explanation
1. Find the side of the square (a):
The diagonal (d) of a square is given by d=a
2
.
14
2
=a
2
⟹a=14cm
Find the radius (r) of the inscribed circle:
When a circle is inscribed inside a square, its diameter is equal to the side length of the square.
Diameter=a=14cm
Radius (r)=
2
a
=
2
14
=7cm
Calculate the area of the circle:
Area=πr
2
=
7
22
×7×7=22×7=154cm
2
The diagonal (d) of a square is given by d=a
2
.
14
2
=a
2
⟹a=14cm
Find the radius (r) of the inscribed circle:
When a circle is inscribed inside a square, its diameter is equal to the side length of the square.
Diameter=a=14cm
Radius (r)=
2
a
=
2
14
=7cm
Calculate the area of the circle:
Area=πr
2
=
7
22
×7×7=22×7=154cm
2