Finding The Perimeter Of A Composite Shape Involving The ... - Nagwa

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Question Video: Finding the Perimeter of a Composite Shape Involving the Circumference of a Semicircle Mathematics

Determine the perimeter of the figure, using 3.14 to approximate 𝜋.

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Video Transcript

Determine the perimeter of the figure, using 3.14 to approximate 𝜋.

The perimeter of any shape is the distance around the outside. In this question, we have three sides of a rectangle and a semicircle. The opposite sides of a rectangle are parallel and equal in length. Therefore, the two vertical sides are 45 centimetres. The perimeter is therefore equal to 45 plus 45 plus 35 plus 𝑥, where 𝑥 is the length of the arc of the semicircle.

The circumference of any circle is equal to 𝜋 multiplied by the diameter or 𝜋𝑑. As a semicircle is half of a circle, the length of the arc of the semicircle will be 𝜋𝑑 divided by two. In our semicircle, the diameter is 35 centimetres. This means that 𝑥 is equal to 𝜋 multiplied by 35 divided by two.

We are told to use 3.14 as an approximation for 𝜋. We need to multiply this by 35 and then divide by two. 3.14 multiplied by 35 is 109.9. Dividing this by two gives us 54.95. The length of the arc of the semicircle is 54.95 centimetres. We can now calculate the total perimeter by adding 45, 45, 35, and 54.95. Adding these four numbers gives us 179.95. The perimeter of the figure is 179.95 centimetres.