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# Semi-circles and quarter circles

The perimeter of a semi-circle can be found by using the equation π x r², which is commonly used to calculate the area of a whole circle:

• area of a semi-circle: 1/2 x π x r2
• area of a quarter circle: 1/4 x π x r2
• perimeter of a semi-circle: π x r + 2 x r
• perimeter of a quarter circle: 1/2 x π x r + 2 x r

Example

A window in the shape of a semi-circle has a radius of 40 cm. Work out:

1. The area
2. The length of the sealant strip needed for the perimeter

Solution

• Area = 1/2 x π x r2

• 1/2 x π x 402

• Area = 2513 cm2

•
• Perimeter = π x r + 2 x r

• π x 40 + 2 x 40

• 125.7 + 80

• Perimeter = 205.7 cm

•

Question

Jenny has a patio in her garden. Its shape is a quarter circle with a radius of 3m.

1. How much space is there on the patio?
2. What is its perimeter?

• We need to find the area.

• Area = 1/4 x π x r2

• 1/4 x π x 32

• Area = 7.07m2

•
• Perimeter = 1/2 x π x r + 2 x r

• 1/2 x π x 3 + 2 x 3

• 4.7 + 6

• Perimeter = 10.7m

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