A) The square area of the side of the house is 533.75 ft.².
B) A sample table comparing three types of paint is as follows:
Type of Price Contains Estimated Coverage
Paint per Gallon Primer per Gallon
Premium $50 Yes 400 sq ft
Standard $30 No 350 sq ft
Economy $20 No 300 sq ft
3) Sally should first calculate the total surface area that needs painting by adding up both areas calculated in step one.
Secondly, she should decide whether she wants to use paint with primer or without, considering that paint with primer might be more expensive but require fewer coats.
Lastly, she should refer to her chosen paint’s estimated coverage per gallon to determine how many gallons she needs to buy.
The rectangle’s width = 35 ft
The rectangle's height = 10 ft
The rectangle's area = 350 sq ft. (35 \times 10
The height of the triangle using trigonometry:
The angle is given = [tex]117.2^\circ[/tex]
The roof's angle with the wall = [tex]31.4^\circ[/tex] (180 - 117.2)/2.
The height (h) can be found using the formula for the tangent of an angle, which is the opposite side (height in our case) divided by the adjacent side (half the base in our case).
Solving for h gives:
h = [tex]\tan(31.4^\circ) \times \frac{35}{2}[/tex]
h = 0.6009 x 35/2
h = 10.5 feet
Substituting the base (35 ft) and the height, the area of the triangle:
A = [tex]\frac{1}{2} \times 35 \times h[/tex]
A = [tex]\frac{1}{2} \times 35 \times 10.5[/tex]
A = 183.75 ft.²
Total Area = 533.75 ft.² (350 + 183.75)
