Question

Find the area of square that can be inscribed in circle of radius 8cm.

Answer 1

The area of a square is [tex]\bold{128 \ \mathrm{cm}^{2}}[/tex]

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.

$A C^{2}=A B^{2}+B C^{2}$

As ABCD is a square all the sides are equal, AB = BC

$A C^{2}=2 A B^{2}$

$A C=\sqrt{2} A B$

$16=\sqrt{2} A B$

$8 \times 2=\sqrt{2} A B$

$A B=8 \sqrt{2}$

Therefore, side of the square is $8 \sqrt{2}$

$\text{Area of square} = a^{2}$

$\text{Area of a square} = (8 \sqrt{2})^{2}=128 \ \mathrm{cm}^{2}$

Answer 2

Step-by-step explanation:

• radius =8cm diameter = 2*8=16cm .Then let side of square be X so a/q Xsq + Xsq =16 sq so Xsq =128 cm sq. It's your answer.