Answer: Third option.
Step-by-step explanation:
Calculate the area of the gate (including the glass panel) which has the shape of a trapezoid.
The formula for calculate the area of a trapezoid is:
[tex]A=\frac{h}{2}(B+b)[/tex]
Where h is the height, B is the larger base and b is the smaller base.
In this case:
[tex]B=10ft\\b=7ft\\h=5ft[/tex]
Substituting, you get:
[tex]A_{gate}=\frac{5ft}{2}(10ft+7ft)=42.5ft^2[/tex]
Calculate the area of the rectangular glass panel, with the formula:
[tex]A_{panel}=l*w[/tex]
Where the lenght is [tex]l=1.43ft[/tex] and the width is [tex]w=0.71ft[/tex]
Then:
[tex]A_{panel}=(1.43ft)(0.71ft)=1.01ft^2[/tex]
The area he needs to paint is:
[tex]A=A_{gate}-A_{panel}\\A=42.5ft^2-1.01ft^2\\A=41.49ft^2[/tex]
If painting the gate costs $2.50 per ft², for 41.49 ft² he will have to spend:
[tex]=(41.49)(\$2.50)\\=\$103.725[/tex]
Therefore the answer is the third option.
