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)=(1)/(2)\pi\cdot r^2`

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

`25.12=(1)/(2)\cdot\pi\cdot r^2`

Dividing both sides by pi:

`(25.12)/(\pi)=(1)/(2)r^2`

Multiplying both sides by 2:

`(2\cdot25.12)/(\pi)=r^2`

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

`\sqrt[]{(2\cdot25.12)/(\pi)}=r`

Switching sides:

`r=\sqrt[]{(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