Question

,Find the Area of the figure below, composed of a rectangle and one semicircle, withanother semicircle removed. Round to the nearest tenths place.158

Answer 1

Step-by-step explanation:

Given:

The figure is composed of a rectangle and one semicircle, with another semicircle removed

The length of the rectangle = 15

the diameter of the semicircle = 8

To find:

the area of the figure

To determine the area of the figure, we will find the area of the rectangle and then subtract the semicircle that was removed from it. Also, we will find the area of the semicircle that is still attached.

Area of a rectangle = length × width

length = 15,

width = diameter of the semicircle = 8

`\begin{gathered} Area\text{ of the rectangle = 15 }*8 \\ Area\text{ of the rectangle = 120} \end{gathered}`

The semicircle on the left side (cut-off) is the same as the semicircle on the right side (attached)

Area of the semicircle = 1/2(area of a circle)

`\begin{gathered} Area\text{ of the semicircle = }(1)/(2)(πr²)\text{ } \\ let\text{ \pi = 3.14} \\ diameter\text{ = 8} \\ diameter\text{ = 2\lparen radius\rparen} \\ radius\text{ = diameter/2} \\ radius\text{ = 8/2 = 4} \\ \\ Area\text{ of the semicircle = }(1)/(2)*3.14*4^2 \\ Area\text{ of the semicircle = 25.12} \end{gathered}`

We will subtract the semicircle from the rectangle as the diagram shows the rectangle is not complete, semic-circle was removed from it

`\begin{gathered} Area\text{ of the rectangle without the semi-circle = 120 - 25.12} \\ \\ Area\text{ of the rectangle without the semi-circle = 94.88} \end{gathered}`

Area of the figure = Area of the rectangle without the semicircle + Area of the semicircle

`\begin{gathered} Area\text{ of the figure = 94.88 + 25.12} \\ \\ Area\text{ of the figure = 120.0 \lparen tenth place\rparen} \end{gathered}`