Assessment and Learning in Knowledge Spaces (ALEKS) Basic Math Placement Practice Test

What are the steps to find the perimeter of a semicircle combined with a rectangle?

1. Find the area of both shapes

2. Find circumference, divide by 2, and add the rectangle's length and width

3. Measure each side individually

4. Calculate only the rectangle's perimeter

The correct answer is: Find circumference, divide by 2, and add the rectangle's length and width

To find the perimeter of a semicircle combined with a rectangle, the approach involves calculating the semicircle's curved edge and adding it to the appropriate sides of the rectangle. First, you would find the circumference of the full circle using the formula \(C = 2\pi r\), where \(r\) is the radius. Since you only need the semicircular part, you divide the circumference by 2, resulting in \(\frac{1}{2}(2\pi r) = \pi r\). Next, it's essential to consider which sides of the rectangle contribute to the total perimeter when combined with the semicircle. Typically, this would involve adding the length of the rectangle plus the diameter of the semicircle (which is \(2r\) for a semicircle with radius \(r\)). So, the perimeter of the semicircle combined with a rectangle is calculated as follows: \[ \text{Perimeter} = \pi r + \text{length of the rectangle} + \text{width of the rectangle} \] Since the semicircle sits on top of the rectangle, you only add the sides of the rectangle that are not in contact with the semicircle. This method of combining