Area & Perimeter

Label our diagram

Solving for the unknowns

$x$ represents half the circumference of a circle with radius $2\ cm$:

$\begin{aligned} x&=\dfrac{2\pi r}{2}\\[0.5em] &=\dfrac{2\pi\left(2\right)}{2}\\[0.5em] &=\dfrac{4\pi}{2}\\[0.5em] &=2\pi \end{aligned}$

$y$ represents the hypotenuse of the right angle triangle:

$\begin{aligned} y^2&=4^2+2^2\\[0.5em] y&=\sqrt{4^2+2^2}\\[0.5em] y&=\sqrt{16+4}\\[0.5em] y&=\sqrt{20}\\[0.5em] y&\approx4.47 \end{aligned}$

Perimeter

$\begin{aligned} P&=5+y+2+5+x\\ &=5+\sqrt{20}+2+5+2\pi\\ &=12+\sqrt{20}+2\pi\\ &\approx22.76 \end{aligned}$

So, the perimeter is approximately 22.76 cm

Area

$\begin{aligned} A&=\text{semi-circle}+\text{rectangle}+\text{triangle}\\[0.5em] &=\left(\dfrac{\pi r^2}{2}\right)+\left(l\times w\right)+\left(\dfrac{b\times h}{2}\right)\\[0.5em] &=\left(\dfrac{\pi \times2^2}{2}\right)+\left(5\times 4\right)+\left(\dfrac{2\times 4}{2}\right)\\[0.5em] &=\left(\dfrac{4\pi}{2}\right)+20+\dfrac{8}{2}\\[0.5em] &=2\pi+20+4\\[0.5em] &\approx 30.28 \end{aligned}$

So, the area is approximately 30.28 cm2