Semicircle area?

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1 Answer
May 8, 2017

The area of the shaded section is 113.076mm^2.

Explanation:

To calculate the area of the shaded area, we calculate the difference between the area of the semicircle and the area of the circle.

The formula for area of the semicircle is:

A_S=(pir_S^2)/2, where A_S=Area of semi-circle, and r_S^2=radius of semicircle, given as 12mm (since 24mm is the diameter which is twice the radius).

The formula for area of the circle is:

A_C=pir_C^2, where A_C=Area of circle, and r_C^2=radius of circle, calculated as 6mm (since the radius of the semicircle forms the diameter of the circle, as can be seen in the diagram).

Hence, to calculate the difference between the two, we write:

A_S-A_C=(pir_S^2)/2-pir_C^2

A_S-A_C=(pixx12^2)/2-pixx6^2

A_S-A_C=(pixx144)/2-pixx36

A_S-A_C=(pixx72)-(pixx36)

A_S-A_C=pi(72-36)

A_S-A_C=pixx36

We consider the value of pi as 3.141.

A_S-A_C=3.141xx36

A_S-A_C=113.076

Since the given diameter is in millimetres, the area will be expressed as square millimetres or mm^2.