Question

Find the area and the perimeter of the shaded regions below. Give your answer as a completely simplified exact value in terms of π (no approximations). The figures below are based on semicircles or quarter circles and problem b), and are involving portions of a square.

Answer 1

What is the perimeter?

Answer 2

So we have a triangle and a semicircle.

If the triangle is equilateral, this is:

AB = BC = 6cm

Then the area of the triangle is equal to (base*height)/2

in this case:

A = (6*6)/2 = 36/2 = 18cm^2.

And the diameter of the semicircle is equal to 6cm, then the diameter is 3cm

And if the area of a circle is A = pi*r^2

then the area of half a circle is:

A = (pi/2*)3^2 = pi*4.5cm^2

Then, the area of the triangle plus the area of the semicircle is:

Total area = 18cm^2 + pi*4.5^2