How to find area of square inscribed in a circle of radius 8 cm?
Answers
If the radius of a circle = 8 cm
.·. Diameter = 8*2 = 16
Diameter of a circle = Diameter of a Square = 16 cm
Area of square = (diagonals)^2 / 2
= 16^2 / 2
= 128 cm^2
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Step-by-step explanation:
Given:
Radius = 8 cm
Step-by-step explanation:
Please find the figure containing a circle of radius 8cm.
ABCD is a square inscribed in the circle.
(OA = OB = OC = OD = 8)
ABC is a right angled triangle, as OA = 8, OB = 8
AB = 8 + 8 = 16
According to Pythagoras theorem,
Square of hypotenuse = Sum of squares of other two sides.
A C^{2}=A B^{2}+B C^{2}AC
2
=AB
2
+BC
2
As ABCD is a square all the sides are equal, AB = BC
A C^{2}=2 A B^{2}AC
2
=2AB
2
A C=\sqrt{2} A BAC=
2
AB
16=\sqrt{2} A B16=
2
AB
8 \times 2=\sqrt{2} A B8×2=
2
AB
A B=8 \sqrt{2}AB=8
2
Therefore, side of the square is 8 \sqrt{2}8
2
\text{Area of square} = a^{2}Area of square=a
2
\text{Area of a square} = (8 \sqrt{2})^{2}=128 \ \mathrm{cm}^{2}Area of a square=(8
2
)
2
=128 cm
2