Question

Find the area of the shaded figure below. Round your answer to one decimal place.534Provide your answer below:square units712

Answer 1

Area of the shaded figure is 77.7 square unit (rounded to 1 decimal place).

Step-by-step explanation

Given:

Rectangle with length = 12 and breadth = 7.

Semi-Circle with diameter = 4

Desired Outcome:

The area of the shaded region.

Looking at the figure carefully, you will notice that it was only half of the circle that was fixed with the rectangle.

Determine the Area of a semi-circle

Area of a semi-circle is half of the area of a circle

`\begin{gathered} Area\text{ \lparen semicircle\rparen= }(1)/(2)\pi r^2\text{ \lparen where r = }(d)/(2)\text{ = 2\rparen} \\ \text{ = }(1)/(2)*3.142*2^2 \\ \text{ = 6.284 unit}^2 \end{gathered}`

Area of the Rectangle

`\begin{gathered} Area\text{ \lparen rectangle\rparen = L}* B \\ \text{ = 12}*7 \\ \text{ = 84 unit}^2 \end{gathered}`

Determine the area of the shaded figure

`\begin{gathered} Area\text{ \lparen shaded\rparen = Area \lparen rectangle\rparen - Area \lparen semicircle\rparen} \\ \text{ = 84 - 6.284} \\ \text{ = 77.716 unit}^2 \end{gathered}`

Hence, the Area of the shaded figure is 77.7 square unit (rounded to 1 decimal place).