Question

1. a half circle is joined to a square with side lengths of 11 units. what is the perimeter of the resulting shape?

Explanation:

Step1: Calculate the perimeter of the square part

The square has 3 sides contributing to the perimeter. Each side is 11 units. So the length from the square part is \(3\times11 = 33\) units.

Step2: Calculate the length of the semicircular arc

The formula for the circumference of a full - circle is \(C = 2\pi r\). For a semicircle, the length of the arc is \(l=\pi r\). Given that the diameter of the semicircle is equal to the side - length of the square (\(d = 11\) units), then the radius \(r=\frac{d}{2}=\frac{11}{2}\) units. Using \(\pi\approx3.14\), the length of the semicircular arc is \(l = 3.14\times\frac{11}{2}=17.27\) units.

Answer:

The perimeter of the resulting shape is \(33 + 17.27=50.27\) units.