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

$\dfrac{bh}{2}=\dfrac{50\cdot 30}{2}=\dfrac{1500}{2}=750$

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

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