Question

this shape is made up of one - half - circle attached to a square with side lengths 15 inches. you can use 3.14 as an approximation for π. what is the approximate perimeter of the entire shape? solve on paper and enter your answer on zearn. you can use your zearn calculator to help you solve.

Explanation:

Step1: Identify the components of the perimeter

The shape is composed of 3 sides of the square and half - circle. The side length of the square $s = 15$ inches.

Step2: Calculate the length of the 3 square - sides

The length of 3 sides of the square is $3\times s=3\times15 = 45$ inches.

Step3: Calculate the circumference of the half - circle

The formula for the circumference of a full circle is $C = 2\pi r$. Since the diameter of the half - circle is equal to the side length of the square ($d = 15$ inches, so $r=\frac{d}{2}=7.5$ inches), the circumference of the half - circle is $\frac{1}{2}\times2\pi r=\pi r$. Using $\pi\approx3.14$ and $r = 7.5$ inches, we get $\frac{1}{2}\times2\times3.14\times7.5=3.14\times7.5 = 23.55$ inches.

Step4: Calculate the perimeter of the entire shape

The perimeter $P$ of the entire shape is the sum of the length of the 3 square - sides and the length of the half - circle arc. So $P=45 + 23.55=68.55$ inches.

Answer:

$68.55$ inches