Question

What is the area of the figure below some help me show the work ;(!

Answer 1

`\large\boxed{\mathtt{Area = 586.2cm^(2).}}`

Explanation:

`\textsf{We are asked to find the area of this figure.}`

`\textsf{In order to make this simpler, draw a line between the rectangle, and the semi-circle.}`

`\textsf{We should identify the formulas needed for the areas of the rectangle, and semi-circle.}`

`\large\underline{\textsf{For the Semi-Circle:}}`

`\mathtt{Area = 1/2( pi(radius)^(2)).}`

`\large\underline{\textsf{For the Rectangle:}}`

`\mathtt{Area = Length \ x \ Width.}`

`\textsf{Let's find the area of the Rectangle first.}`

`\mathtt{Area = 15 \ x \ 24}`

`\mathtt{Area = 360cm^(2).}`

`\textsf{For the Semi-Circle, the radius is 1/2 of the Diameter. (24)}`

`\mathtt{Area = 1/2( pi(12)^(2)).}`

`\mathtt{Area = 1/2(144 \pi).}`

`\mathtt{Area = 72 \pi.}`

`\mathtt{Area \approx 226.2cm^(2).}`

`\textsf{Add the areas together to represent the area of the figure.}`

`\large\underline{\textsf{Add:}}`

`\mathtt{360cm^(2) + 226.2cm^(2) = 586.2cm^(2). }`

`\large\boxed{\mathtt{Area = 586.2cm^(2).}}`