Question

(Please reference attached photo for problem.)Show your work please. Also, What is the perimeter?

Answer 1

Given the shape below:

The above shape is a combination of a semicircle and a rectangle labeled as A and B respectively.

To find the perimeter of the shape:

step 1: Evaluate the perimeter of the circle.

The perimeter of the semicircle is expressed as

`\begin{gathered} perimeter\text{ of semicircle=2}\pi r \\ where\text{ r is the radius} \\ \pi\Rightarrow3.14 \end{gathered}`

Thus, we have

`\begin{gathered} perimeter=2*3.14*((10)/(2)) \\ =31.4\text{ cm} \end{gathered}`

step 2: Evaluate the perimeter of the rectangle.

The perimeter of the rectangle is expressed as

`\begin{gathered} perimeter=2(l+w) \\ where \\ l\Rightarrow length \\ w\Rightarrow width \end{gathered}`

In this case, we have

`\begin{gathered} l=10\text{ cm} \\ w=4\text{ cm} \\ thus, \\ Perimeter\text{ = 2\lparen10+4\rparen} \\ =2(14) \\ =28\text{ cm} \end{gathered}`

step 3: Sum up the perimeters.

Thus, we have

`\begin{gathered} perimeter\text{ of shape = perimeter of circle + perimeter of rectangle} \\ =31.4+28 \\ \Rightarrow perimeter\text{ of shape = 59.4 cm} \end{gathered}`

Hence, the perimeter of the shape is evaluated to be

`59.4\text{ cm}`