Question

A rectangle, a triangle, and two congruent semicircles were used to form the figure shown. Rectangle 5cm,20cmcircle : radius 5cm,pi=3.14Triangle: base 10cm,8cmWhich measurement is closest to the area of the figure in square centimeters?

Answer 1

The area of a shape is the amount of space it occupies

Step 1:

We start by calculating the area of the rectangle using:

`\begin{gathered} A_(rectangle)=l* b \\ \end{gathered}`

By substituting the values, we will have

`\begin{gathered} A_(rectangle)=l* b \\ A_(rectangle)=20cm*5cm \\ A_(rectangle)=100cm^2 \\ A_1=100cm^2 \end{gathered}`

Step 2:

we calculate the area of the triangle using:

`A_(triangle)=(1)/(2)* base* height`

By substituting the values, we will have

`\begin{gathered} A_(tr\imaginaryI angle)=(1)/(2)* base* he\imaginaryI ght \\ A_{tr\mathrm{i}angle}=(1)/(2)*10cm*8cm \\ A_{tr\mathrm{i}angle}=(80cm^2)/(2) \\ A_{tr\mathrm{i}angle}=40cm^2 \\ A_2=40cm^2 \end{gathered}`

Step 3:

Calculate the area of the two semicircles

`A_(semicircle)=(\pi r^2)/(2)`

By substituting the values, we will have

`\begin{gathered} A_(sem\imaginaryI c\imaginaryI rcle)=(\pi r^(2))/(2) \\ A_{sem\mathrm{i}c\mathrm{i}rcle}=3.14*(5^2)/(2) \\ A_{sem\mathrm{i}c\mathrm{i}rcle}=39.25cm^2 \\ Area\text{ of two semicircle will be} \\ A_3=39.25cm^2*2 \\ A_3=78.5cm^2 \end{gathered}`

Step 4:

Calculate the area of the shape

We will calculate the area of the shape by adding all the individual areas together

`A_(shape)=A_1+A_2+A_3`

By substituting the values, we will have

`\begin{gathered} A_(shape)=A_(1)+A_(2)+A_(3) \\ A_(shape)=100cm^2+40cm^2+78.5cm^2 \\ A_(shape)=218.5cm^3 \end{gathered}`

Hence,

The area of the shape will be

`\Rightarrow218.5cm^2`