The perimeter of a semicircle is 20.56 metres. What is the semicircle's area?

The perimeter of a semicircle is given by the formula P = πr + 2r, where r is the radius of the semicircle.

Given that the perimeter is 20.56 metres, we can set up the equation:

20.56 = πr + 2r

To solve for r, we first combine like terms:

20.56 = r(π + 2)

Then, we divide both sides by (π + 2) to isolate r:

r = 20.56 / (π + 2)

Using the approximation π ≈ 3.14, we find:

r ≈ 20.56 / (3.14 + 2) ≈ 20.56 / 5.14 ≈ 4 metres

The area of a semicircle is given by the formula A = 0.5πr². Substituting r ≈ 4 metres, we find:

A ≈ 0.5 * 3.14 * (4)² ≈ 0.5 * 3.14 * 16 ≈ 25.12 square metres

So, the area of the semicircle is approximately 25.12 square metres.