Combine like terms
x^2 + 2x + 3 + 3x^2 + x + 1
4x^2 + 3x + 4
Answer:
The area of the house is ![136.13\ ft^2](https://tex.z-dn.net/?f=136.13%5C%20ft%5E2)
Step-by-step explanation:
we know that
The area of the floor plan of the house is equal to the area of one rectangle plus the area of a trapezoid plus the area of semicircle
so
step 1
Find the area of the large rectangle
![A=LW](https://tex.z-dn.net/?f=A%3DLW)
we have
![L=13\ ft\\W=8\ ft](https://tex.z-dn.net/?f=L%3D13%5C%20ft%5C%5CW%3D8%5C%20ft)
substitute
![A=(13)(8)=104\ ft^2](https://tex.z-dn.net/?f=A%3D%2813%29%288%29%3D104%5C%20ft%5E2)
step 2
Find the area of trapezoid
The area of trapezoid is equal to
![A=\frac{1}{2}[b_1+b_2]h](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5Bb_1%2Bb_2%5Dh)
we have
![b_1=5\ ft\\b_2=7\ ft\\h=3\ ft](https://tex.z-dn.net/?f=b_1%3D5%5C%20ft%5C%5Cb_2%3D7%5C%20ft%5C%5Ch%3D3%5C%20ft)
substitute
![A=\frac{1}{2}[5+7]3=18\ ft^2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%5B5%2B7%5D3%3D18%5C%20ft%5E2)
step 3
Find the area of semicircle
The area of semicircle is
![A=\frac{1}{2} \pi r^{2}](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%20%5Cpi%20r%5E%7B2%7D)
we have
![r=3\ ft](https://tex.z-dn.net/?f=r%3D3%5C%20ft)
substitute
![A=\frac{1}{2} (3.14)(3)^{2}=14.13\ ft^2](https://tex.z-dn.net/?f=A%3D%5Cfrac%7B1%7D%7B2%7D%20%283.14%29%283%29%5E%7B2%7D%3D14.13%5C%20ft%5E2)
step 4
Adds the areas
![A=104+18+14.13=136.13\ ft^2](https://tex.z-dn.net/?f=A%3D104%2B18%2B14.13%3D136.13%5C%20ft%5E2)
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