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Find the area of the figure below Braun your answer to one decimal place

Find the area of the figure below Braun your answer to one decimal place-example-1
User Miklesw
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1 Answer

23 votes
23 votes

To determine the area of the figure you have to decompose it into two simpler figures:

A semicircle (green) and a rectangle (blue)

The total area of the figure is equal to the area of the semicircle plus the area of the rectangle


A_T=A_C+A_R

The area of the rectangle can be calculated as


\begin{gathered} A_R=w\cdot l \\ A_R=6\cdot12 \\ A_R=72 \end{gathered}

The area of a circle can be calculated as


\text{Acircle}=\pi r^2

To calculate the area of the semicircle you have to divide it by 2


A_C=(\pi r^2)/(2)

The semicircle has a diameter of d=6

So the radius is


r=(d)/(2)=(6)/(2)=3

The area of the semicircle is


\begin{gathered} A_C=(\pi r^2)/(2) \\ A_C=(\pi3^2)/(2) \\ A_C=(9)/(2)\pi \end{gathered}

Finally add both areas to determine the area of the figure


\begin{gathered} A_T=A_R+A_C \\ A_T=72+(9)/(2)\pi \\ A_T=86.137\cong86.1 \end{gathered}

The total area of the figure is 86.1

Find the area of the figure below Braun your answer to one decimal place-example-1
User Tomas By
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3.1k points