Measurement: Area of Circle


Trace a circular shape on paper and cut it along the edge. Fold it in half, then fold it 3 more times so you have 16 folding lines meeting at the centre like below.

area of circle


Cut the circle along the folding lines to get 16 slices (sectors) and arrange them as below.

area of circle


The circle is roughly arranged into a rectangle so their areas are now the same.

Area of the circle  =  Area of the rectangle
   =  Length × Breadth
   =  π × Radius × Radius
Area of Circle = π × Radius × Radius

Problem 1

What is the area of a circular field of radius 49 m?
find area of circle

Area  =  22
71
 × 497 × 49
   =  7546 m2

Problem 2

The diameter of a circular frisbee is 24 cm. Find its area. Give your answer in terms of π.
find area of circle

Diameter  =  24 cm
Radius  =  24 ÷ 2
   =  12 cm
Area  =  π × 12 × 12
   =  144 π cm2

Problem 3

The diameter of a semicircle is 5 cm. What is its area?
find area of semicircle

Radius  =  5 cm ÷ 2
   =  2.5 cm
Area of a semicircle  =  Half of the area of the circle
   =  1
2
 × 3.14 × 2.5 × 2.5
   =  9.81 cm2


Problem 4

Find the area of a quadrant whose radius is 7 m.
find area of quadrant

Area of a quadrant  =  A quarter of the area of the circle
   =  
1
42
 × 1122
  17
  ×  71 × 7
   =  38.5 m2


Problem 5

Find the area of the fan below made of 4 identical quadrants and a circle.
find area of figure

Area of the middle circle  =  3.14 × 6 × 6
   =  113.04 cm2

4 quadrants of radius 12 cm together make 1 circle of radius 12 cm.
Area of 4 quadrants  =  Area of 1 circle
   =  3.14 × 12 × 12
   =  452.16 cm2

Area of fan  =  113.04 + 452.16
   =  565.2 cm2