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

Answer:

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

Step 1:

We start by calculating the area of the rectangle using:

$\begin{gathered} A_{rectangle}=l\times b \\ \end{gathered}$

By substituting the values, we will have

$\begin{gathered} A_{rectangle}=l\times b \\ A_{rectangle}=20cm\times5cm \\ A_{rectangle}=100cm^2 \\ A_1=100cm^2 \end{gathered}$

Step 2:

we calculate the area of the triangle using:

$A_{triangle}=\frac{1}{2}\times base\times height$

By substituting the values, we will have

$\begin{gathered} A_{tr\imaginaryI angle}=\frac{1}{2}\times base\times he\imaginaryI ght \\ A_{tr\mathrm{i}angle}=\frac{1}{2}\times10cm\times8cm \\ A_{tr\mathrm{i}angle}=\frac{80cm^2}{2} \\ A_{tr\mathrm{i}angle}=40cm^2 \\ A_2=40cm^2 \end{gathered}$

Step 3:

Calculate the area of the two semicircles

$A_{semicircle}=\frac{\pi r^2}{2}$

By substituting the values, we will have

$\begin{gathered} A_{sem\imaginaryI c\imaginaryI rcle}=\frac{\pi r^{2}}{2} \\ A_{sem\mathrm{i}c\mathrm{i}rcle}=3.14\times\frac{5^2}{2} \\ A_{sem\mathrm{i}c\mathrm{i}rcle}=39.25cm^2 \\ Area\text{ of two semicircle will be} \\ A_3=39.25cm^2\times2 \\ A_3=78.5cm^2 \end{gathered}$

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

$\Rightarrow218.5cm^2$