Question

1. determine the area and perimeter of the shape in the figure. measurements are in centimeters. round both results to the nearest 100th (you will need a calculator).

Explanation:

Step1: Calculate the area of the semi - circle

The area formula for a full - circle is $A_{circle}=\pi r^{2}$, for a semi - circle $A_{semicircle}=\frac{1}{2}\pi r^{2}$. Here $r = 5$, so $A_{semicircle}=\frac{1}{2}\pi(5)^{2}=\frac{25\pi}{2}\approx39.27$ square centimeters.

Step2: Calculate the area of the rectangle

The area formula for a rectangle is $A_{rectangle}=l\times w$. Here $l = 10$ and $w = 4$, so $A_{rectangle}=10\times4 = 40$ square centimeters.

Step3: Calculate the total area of the shape

$A = A_{semicircle}+A_{rectangle}=\frac{25\pi}{2}+40\approx39.27 + 40=79.27$ square centimeters.

Step4: Calculate the perimeter of the semi - circle

The formula for the circumference of a full - circle is $C = 2\pi r$, for a semi - circle $C_{semicircle}=\pi r$. Here $r = 5$, so $C_{semicircle}=5\pi\approx15.71$ centimeters.

Step5: Calculate the lengths of the non - circular parts of the perimeter

The non - circular parts of the perimeter include two lengths of 10 centimeters and one length of 4 centimeters. The sum of these lengths is $10 + 10+4=24$ centimeters.

Step6: Calculate the total perimeter of the shape

$P = C_{semicircle}+24=5\pi + 24\approx15.71+24 = 39.71$ centimeters.

Answer:

Area: $79.27$ square centimeters, Perimeter: $39.71$ centimeters