Question

Find the area for these 2 shapes (b&c)

Answer 1

The first shape is a right triangle composed with a semi circle.

The right triangle has a height of 50cm, and its base is the diameter of the circle, which is twice the radius, which is 30cm.

So, the area of the triangle is

`(bh)/(2)=(50\cdot 30)/(2)=(1500)/(2)=750`

The area of the circle is simply

`\pi r^2 = \pi\cdot 15^2 = 225\pi`

So, the area of the shape is

`750+225\pi=75(10+3\pi)`

The second shape is the difference between an outer circle and an inner one. The area is thus the difference of the two areas: let
`r_o` be the outer radius and
`r_i` be the inner one. The area of the shape is

`\pi r_o^2-\pi r_i^2=\pi(r_0^2-r_i^2) = \pi(90^2-40^2)=6500\pi`