Question

A rectangle is placed around a semi circle as shown below the length of the rectangle is 12mm. Find The area of the shaded region. Use the value 3.14 for pi, and do not round your answer be sure to include the correct unit in your answer.

Answer 1

Explanation

We are given a rectangle placed around a semi-circle as shw in the image below:

We are required to determine the area of the shaded portion.

This is achieved thus:

The area of the shaded portion is given as:

`\begin{gathered} Area=Area\text{ }of\text{ }rectangle-Area\text{ }of\text{ }semicircle \\ Area=A_r-A_s \end{gathered}`

The dimension of the rectangle is given as:

`\begin{gathered} Length=Diameter\text{ }of\text{ }the\text{ }semicircle=12mm \\ Width=Radius\text{ }of\text{ }the\text{ }semicircle=(12)/(2)=6mm \end{gathered}`

Therefore, the area of the shaded portion is:

`\begin{gathered} Area=A_r-A_s \\ Area=(l* w)-((\pi r^2)/(2)) \\ Area=(12*6)-((3.14*6^2)/(2)) \\ Area=(72)-(56.52) \\ Area=15.48mm^2 \end{gathered}`

Hence, the answer is:

`Area=15.48mm^(2)`