Question

Calculate the perimeter of the shaded region in the diagram showing a semicircle inside a rectangle. The rectangle has a length of 150m, and the semicircle touches the rectangle at points A, B, and C. Give your answer correct to 3 significant figures.

A) 362.256m
B) 429.167m
C) 327.273m
D) 321.432m

Answer 1

To calculate the perimeter of the shaded region, add the length of the rectangle to the circumference of the semicircle. The perimeter is given by (2 + pi) * radius.

Step-by-step explanation:

To calculate the perimeter of the shaded region, we need to find the lengths of all the sides. First, let's find the length of side CD of the rectangle. The length of the rectangle is given as 150m, and since the semicircle touches the rectangle at points C and D, CD is equal to the diameter of the semicircle. The diameter is twice the radius of the semicircle, so CD = 2 * AB = 2 * radius.

Next, let's find the circumference of the semicircle. The formula for the circumference of a circle is 2 * pi * radius. Since we only have half of the circle, we divide the formula by 2. So the circumference of the semicircle is pi * radius.

Finally, to find the perimeter of the shaded region, we sum the length of the rectangle (CD) and the circumference of the semicircle. So, the perimeter = CD + circumference = 2 * radius + pi * radius = (2 + pi) * radius.