Question

3 - 116. find the area and perimeter of the shape below. show your work.3 - 117. this problem is a checkpoint for unit rates and proportions. it will be referred to as checkpoint 3. in parts (a) through (c), use the given information to find the unit rate. in parts (d) through (f), write and solve a proportion based on the given information.a. if 2 1/4 pounds of bananas cost $1.89, what is the cost per pound?

Explanation:

Step1: Calculate the area

The shape is composed of a rectangle and a circle.

• Rectangle area: The formula for the area of a rectangle is \(A_{rectangle}=l\times w\). Here, \(l = 6m\) and \(w=2\times1.8m = 3.6m\), so \(A_{rectangle}=6\times3.6=21.6m^{2}\).
• Circle area: The formula for the area of a circle is \(A_{circle}=\pi r^{2}\), where \(r = 1.8m\). So \(A_{circle}=\pi\times(1.8)^{2}=3.24\pi m^{2}\approx3.24\times3.14 = 10.1736m^{2}\).
• Total area: \(A = A_{rectangle}+A_{circle}=21.6 + 10.1736=31.7736m^{2}\).

Step2: Calculate the perimeter

The perimeter is composed of two lengths of the rectangle and the circumference of a circle.

• Circumference of the circle: The formula for the circumference of a circle is \(C = 2\pi r\), with \(r = 1.8m\), so \(C=2\pi\times1.8 = 3.6\pi m\approx3.6\times3.14=11.304m\).
• Lengths of the rectangle: There are two lengths of the rectangle, each of length \(l = 6m\), so the total length is \(2\times6=12m\).
• Total perimeter: \(P=12 + 11.304=23.304m\).

Answer:

The area is approximately \(31.77m^{2}\) and the perimeter is approximately \(23.30m\).