Question

A landscape designer wants to include a semicircular patio at the end of a square sandbox she knows that the area of the semicircular patio is 25.12 cm squared

Answer 1

EXPLANATION

Let's see the facts:

The Area is 25.12cm^2

The Area of the circle is given by the following equation:

$\text{Area}_{semicircle}=\frac{1}{2}\pi\cdot r^2$

We need to isolate r in order to get the length of the side:

$25.12=\frac{1}{2}\cdot\pi\cdot r^2$

Dividing both sides by pi:

$\frac{25.12}{\pi}=\frac{1}{2}r^2$

Multiplying both sides by 2:

$\frac{2\cdot25.12}{\pi}=r^2$

Now, we need to apply the square root to both sides:

$\sqrt[]{\frac{2\cdot25.12}{\pi}}=r$

Switching sides:

$r=\sqrt[]{\frac{50.24}{\pi}}=\sqrt[]{16}$

Simplifying the square root:

$r=4$

The radius is r=4, but the diameter of the semicircle is equivalent to the side of the square so,

Side of square = Diameter of semicircle = 2*4 = 8

The answer is 8cm