Question

The figure below shows two half-circles at the ends of a rectangle with the dimensions shown.

Answer 1

`A_T=94.63in^2`

Explanation We need to find the are of the figure provided, the area is composed of three parts, rectangle, and two half circles: therefore the total area would be the sum of the three:

Area Rectangle:

`A_R=w* l=15in*5in=75in^2`

Area of two half circles:

`\begin{gathered} A_c=\pi r^2_{} \\ r=(5)/(2)in=2.5in \\ \therefore\rightarrow \\ A_c=\pi(2.5in)^2=(3.141*6.25)in^2=19.63in^2 \\ \therefore\rightarrow \\ A_(C.H)=(19.63)/(2)in^2=9.82in^2 \\ \text{ SInce We have two such halves, therefore the total are of the two is} \\ A_(C-T)=2*9.82in^2=19.63in^2 \end{gathered}`

The total area of the figure is:

`\begin{gathered} A_T=A_R+A_(C-T)=75in^2+19.63in^2=94.63in^2 \\ A_T=94.63in^2 \end{gathered}`