
Area of a circle = \( \scriptsize \pi r^2 \)
We can also find the area given the diameter
the radius of a circle is half of its diameter
r = \( \frac{d}{2} \)
We can substitute this into Area of a circle = \( \scriptsize \pi r^2 \)
Therefore Area = \(\scriptsize \pi \: \times \: \normalsize \frac{d}{2} \scriptsize \: \times \: \normalsize \frac{d}{2} \\ = \frac{\pi d^2}{4} \)

To calculate the Area of a Semi-circle, divide the area of a circle by 2 (as two semi-circles make a circle). We get, \( \frac{1}{2} \; \times \; \scriptsize \pi r^2 \)

To calculate the Area of a Quadrant, divide the area of a circle by 4 (as four quadrants make a circle). We get, \( \frac{ \pi r^2}{4} \)
Example 1:
Find the area of a circle with a radius of 3.5cm.
\( \left ( \scriptsize \pi = \normalsize \frac{22}{7} \right) \)
Solution:
r = \( \scriptsize 3.5 \: or \: \normalsize \frac{35}{10} \)
Area of a circle = \( \scriptsize \pi r^2 \)
Area of a circle = \( \frac{22}{7} \; \times \; \frac{35}{10} \; \times \; \frac{35}{10} \)
= \( \frac{22 \; \times \; 5 \; \times \; 35}{10 \; \times \; 10} \)
= \( \frac{3850}{100} \)
= \( \scriptsize 38.50 cm^2 \)
or
⇒ \( \scriptsize \pi r^2 = \normalsize \frac{22}{7} \scriptsize\; \times \; 3.5 \; \times \; 3.5 \)
= \( \frac{269.5}{7} \)
= \( \scriptsize 38.5 cm^2 \)
Example 2:
Find the area of a semicircle with a diameter of 22mm.
\( \left ( \scriptsize \pi = \normalsize \frac{22}{7} \right) \)
Note: Radius = \( \frac{diameter}{2}\)
r = \( \frac{d}{2}\)
From the question, d = 22 mm
r = \( \frac{d}{2}\)
r = \( \frac{22}{2}\)
r = 11 mm
Area of a semicircle = ½ x area of a circle
Area of a semicircle = ½ x πr2.
Area of a semicircle = \( \frac{1}{2} \; \times \; \frac{22}{7} \; \times \; \scriptsize (11)^2 \)
= \( \frac{1}{2} \; \times \; \frac{22}{7} \; \times \; \scriptsize 11 \; \times \; 11 \)
= \( \frac{11\; \times \; 11 \; \times \; 11}{7} \)
= \( \frac{1331}{7} \)
Area of a semicircle = 190.1 mm2
or
Area = \( \frac{\pi d^2}{4} \)
d = 22 mm
Therefore, Area = \( \frac{\pi \; \times \; 22^2}{4} \)
= \( \frac{ \frac{22}{7} \; \times \; 22 \; \times \; 22}{4} \)
= \( \frac{ 22 \; \times \; 22 \; \times \; 22}{28} \)
Area = \( \frac{ 10648}{28} \)
Area = 380.3
Area of a semicircle = ½ x area of a circle.
Area of a semicircle = \( \frac{1}{2} \; \times \; \scriptsize 380.3 \)
Area of a semicircle = 190.1 mm2
Example 3:
Find the area of a circular shape which has a circumference of 21.89m.
\( \left ( \scriptsize \pi = 3.14 \right)\)
Solution:
The circumference of a circle is given by:
C = πd
d = \( \frac{C}{\pi} \)
C = 21.89m,
π = 3.14
d = \( \frac{21.89}{3.14} \)
d = 6.97m
So radius = \( \frac{d}{2} \)
= \( \frac{6.97}{2} \)
= 3.49m
Area of a circle = \(\scriptsize \pi r^2\)
= 3.14 × (3.49)2
= 3.14 × 3.49 × 3.49
= 38.2m
The area of the circle is 38.2m
Example 4:
Calculate the area of each of the following shapes:
⇒ \( \left ( \scriptsize \pi = \normalsize \frac{22}{7} \right) \)

(a)
Area = πr2
Area of a semi-circle = \( \frac{\pi r^2}{2} \)
radius is half of the diameter, from the question diameter, d = 28cm
∴ r = \( \frac{d}{2} \)
r = \( \frac{28}{2} \)
r = \( \scriptsize 14 \: cm \)
Area = πr2
Area = \( \frac{22}{7} \; \times \; \scriptsize 14 \; \times \; \times \; 14 \)
= 22 × 2 × 14
= 616cm2
Area of semi-circle = \( \frac{616cm^2}{2} \)
Area of semi-circle = \( \scriptsize 308cm^2 \)
(b)
Area of circle = \(\scriptsize \pi r^2\)
Area of quadrant = \( \frac{\pi r^2}{4} \)
⇒ \( \scriptsize \pi = \normalsize \frac{22}{7}\scriptsize, \; r = 7 \)
Area = \( \frac{22}{7} \; \times \; \scriptsize 7 \; \times \; 7 \)
= \( \scriptsize 22 \; \times \; 7 \)
= \( \scriptsize 154cm^2 \)
Area of a quadrant = \( \frac{154}{4} \)
= \( \scriptsize 38.5cm^2 \)
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