Question

The blueprint below is a rectangular living room that has semicircular sitting area attached to it. What is the area of the figure in the blue print? Show or explain how you got your answer. The number covered is 16 ft incase you can't see it! :)

Answer 1

`\text{total area=248.54 square f}eet`

Step-by-step explanation

to find the area of the shape we can divide it in two more known shapes

a rectangle+ half circle

so,

`\begin{gathered} \text{total area= area of the rectangle+areaof half circle} \\ \text{total area=(width}\cdot length)+(\pi\cdot radius^2)/(2) \\ \\ \text{radius}=(diameter)/(2) \\ \text{total area=(width}\cdot length)+(\pi\cdot((diameter)/(2))^2)/(2) \\ \text{total area=(width}\cdot length)+(\pi\cdot(d^2)/(4))/(2) \\ \text{total area=(width}\cdot length)+((d^2\cdot\pi)/(4))/(2) \\ \text{total area=(width}\cdot length)+(d^2\cdot\pi)/(8) \end{gathered}`

Let

width=12

length=16

diameter=12

Step 2

replace,

`\begin{gathered} \text{total area=(width}\cdot length)+(d^2\cdot\pi)/(8) \\ \text{total area=(12}\cdot16)+(12^2\cdot\pi)/(8) \\ \text{total area=192+}(144\pi)/(8) \\ \text{total area=192+56.54} \\ \text{total area=248.54 square f}eet \end{gathered}`

I hope this helps you