Question

Find the area of a square inscribed in a circle of radius 8 cm.

• A. 64 cm²
• B. 136 cm²
• C. 144 cm²
• D. 128 cm²

Answer 1

Answer:

D. 128 cm²

For a square inscribed in a circle, the diagonal of the square equals the diameter of the circle.

• Radius of the circle (= 8) cm

• Diameter (= 16) cm

Using the Pythagorean relationship for a square:

genui{"geometry_measurement_learning_block":{"type_id":"PYTHAGOREAN_THEOREM"}}

If the side of the square is (s), then:

$s\sqrt{2}=16$
$s=\frac{16}{\sqrt{2}}=8\sqrt{2}\text{ cm}$

Area of the square:

$s^2=(8\sqrt{2})^2=64\times 2=128\text{ cm}^2$