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

1 Answer
Jun 18, 2018

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.