Question

The area of the square is 100 square centimeters. What is the area of the circle?

Answer 1

Answer:

• Since the question is incomplete, see the figure attached and the explanation below.

Explanation:

Since the figure is missing, I enclose the figure of a square inscribed in a circle.

Since the area of a square is the side length squared, you can determine the side length:

• Area = (side length)²

• 100 cm² = (side lenght)²

        $side\text{ }length=\sqrt{100cm^2}=10cm$

From the side length, you can find the diagonal of the square, which is equal to the diameter of the circle, using the Pythagorean theorem:

• diagonal² = (10cm)² + (10cm)² = 2 × (10cm)²

         $diagonal=\sqrt{2\times (10cm)^2}\\ \\ diagonal=10\sqrt{2} cm$

The area of the circle is π (radius)².

• radius = diameter/2 = diagonal/2

        $area= \pi \times (5\sqrt{2}cm)^2=50\pi cm^2$