Question

By considering total area as the sum of the areas of all of its parts, we can determine the area of a figure such as the one to the right. Find the total area of the figure to the right. Use 3.14 as an approximation for π.A = ___ (units^3, units, units^2)(Type an integer or a decimal)

Answer 1

The area of the composite figure is equivalent to 15.14units³

The volume of the composite figure is equivalent to the sum of the two semicircle and a triangle

Area of the 2 semicircles = πr²

Area of the 2 semicircles = 3.14(1)²

Area of the 2 semicircles = 3.14units³

Area of the rectangle = length * width

Area of the rectangle = 12 * 1

Area of rectangle = 12units³

Hence the area of the composite figure = 3.14 + 12

Area of the composite figure = 15.14 units³

Hence the area of the composite figure is equivalent to 15.14units³

Answer 2

Concept: To calculate the area of the fugure, we are going to calculate the area of the two semicircles and also calculate the area of the rectangle and then add them up together

The formula used to calculate the area of a semicircle is

`\begin{gathered} A_{\text{semicircle}}=(\pi r^2)/(2) \\ \text{where,} \\ \pi=3.14 \\ r=1 \end{gathered}`

The formula used to calculate the area of a rectangle is

`\begin{gathered} A_{\text{rectangle}}\rbrack=\text{length}* breadth \\ \text{where,} \\ \text{length}=12 \\ \text{breadth}=1+1=2 \end{gathered}`

By substituting the values in the formulas, we will have

`\begin{gathered} A_{\text{semicircle}}=(\pi r^2)/(2) \\ A_{\text{semicircle}}=3.14*1^2 \\ A_{\text{semicircle}}=3.14\text{unit}^2 \end{gathered}`
`\begin{gathered} A_{\text{rectangle}}\rbrack=\text{length}* breadth \\ A_{\text{rectangle}}=12*2 \\ A_{\text{rectangle}}=24\text{unit}^2 \end{gathered}`

Hence,

The area of the shape will be

`=A_{\text{rectangle}}+A_{\text{semicircle}}+A_{\text{semicircle}}`

By substituting the values, we will have

`\begin{gathered} =A_{\text{rectangle}}+A_{\text{semicircle}}+A_{\text{semicircle}} \\ =24\text{unit}^2+3.14\text{unit}^2+3.14\text{unit}^2 \\ =30.28\text{units}^2 \end{gathered}`

Hence,

The final answer is = 30.28unit²