Question

The area of a semi circle is 130cm. Find it's total perimeter?

Answer 1

`sqrt(130/pi)(pi+2)=33.1 cm` to three significant figures.

Explanation:

The units are wrong in the question - an area must have square units, not unsquared units of length. I assume that it should read "130 `cm^2`"?

The area of a circle is `pir^2`, where `r` is its radius, and so the area of a semicircle is half that, `pi/2r^2`.

The perimeter of a semicircle is half the circumference of the circle (whole circumference = `2pir`) plus two radii, across the middle: `pir+2r=r(pi+2)`.

So we deduce the radius `r` from the area:
`130=pir^2`, so `r=sqrt(130/pi)`
and then deduce the perimeter from the radius:
`sqrt(130/pi)(pi+2)`

Numerically, this is 33.1 cm, to three significant figures.