Area & Circumference of Circles (Edexcel IGCSE Maths B): Revision Note

Remember that area is always measured in square units (cm², m², ... etc.) and circumference is always measured in units of a single length (cm, m, ... etc.)

Find the area and perimeter of the semicircle shown in the diagram.

Give your answers in terms of $\pi$.

Answer:

 The area of a semicircle is half the area of the full circle with the same diameter, so begin by finding the area of the full circle

Find the radius by dividing the diameter by 2

$r=\frac{16}{2}=8\mathrm{cm}$

Substitute this into the formula for the area of a circle $A=\pi r^2$.
Leave your answer in terms of $\pi$, (this just means do not multiply by $\pi$  on your calculator) 

$A_{\mathrm{full}\mathrm{circle}}=\pi {\left(8\right)}^2=64\pi$

Find the area of the semicircle by dividing the full area by 2

$A_{\mathrm{semicircle}}=\frac{1}{2}\left(64\pi \right)=\frac{64}{2}\pi =32\pi$

Area = 32π cm²

The perimeter of the semicircle is made up of both the arc of the circle (half of the circumference) and the diameter of the semicircle

Find the full length of the circumference of the circle using the formula 

$C=2\pi r$  (or $C=\pi d$)

Substitute the radius = 8 cm into the formula
Again, leave your answer in terms of $\pi$

$C=2\pi \left(8\right)=16\pi$

Find the length of the arc (the curved part of the perimeter of the semicircle) by dividing the full area by 2

$\mathrm{Curved}\mathrm{length}=\frac{1}{2}\left(16\pi \right)=\frac{16}{2}\pi =8\pi$

Find the full perimeter by adding this to the length of the diameter of the circle

Perimeter = (8π+16) cm