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A rectangle, 6 cm by 3 cm, and a semi-circle are joined to make this shape - OCR - GCSE Maths - Question 11 - 2021 - Paper 1

Question 11

A rectangle, 6 cm by 3 cm, and a semi-circle are joined to make this shape. Work out the area of the shape.

Worked Solution & Example Answer:A rectangle, 6 cm by 3 cm, and a semi-circle are joined to make this shape - OCR - GCSE Maths - Question 11 - 2021 - Paper 1

Step 1

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Answer

The area of a rectangle is calculated using the formula:

$ext{Area}_{rectangle} = ext{length} imes ext{width}$

Here, the length is 6 cm and width is 3 cm:

$ext{Area}_{rectangle} = 6 imes 3 = 18 ext{ cm}^2$

Step 2

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Answer

The area of a circle is given by:

$ext{Area}_{circle} = rac{1}{2} imes ext{π} r^2$

For the semi-circle, the radius (r) is half of the width of the rectangle:

$r = rac{3}{2} = 1.5 ext{ cm}$

Thus, the area of the semi-circle is:

$ext{Area}_{semi-circle} = rac{1}{2} imes ext{π} (1.5)^2 = rac{1}{2} imes ext{π} imes 2.25 = 3.375 ext{ cm}^2$

Step 3

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Answer

Now, sum the areas of the rectangle and the semi-circle:

$ext{Total Area} = ext{Area}_{rectangle} + ext{Area}_{semi-circle}$

Substituting the values:

$ext{Total Area} = 18 + 3.375 = 21.375 ext{ cm}^2$

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