Answer:
[tex]2\ gal[/tex]
Step-by-step explanation:
we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
we have
[tex]A(18,20),B(4,20),C(4,4),D(16.2),E(22.10)[/tex]
step 1
Find the distance AB
we have
[tex]A(18,20),B(4,20)[/tex]
substitute in the formula
[tex]d=\sqrt{(20-20)^{2}+(4-18)^{2}}[/tex]
[tex]d=\sqrt{(0)^{2}+(-14)^{2}}[/tex]
[tex]AB=14\ ft[/tex]
step 2
Find the distance BC
we have
[tex]B(4,20),C(4,4)[/tex]
substitute in the formula
[tex]d=\sqrt{(4-20)^{2}+(4-4)^{2}}[/tex]
[tex]d=\sqrt{(-16)^{2}+(0)^{2}}[/tex]
[tex]BC=16\ ft[/tex]
step 3
Find the distance DE
we have
[tex]D(16.2),E(22.10)[/tex]
substitute in the formula
[tex]d=\sqrt{(10-2)^{2}+(22-16)^{2}}[/tex]
[tex]d=\sqrt{(8)^{2}+(6)^{2}}[/tex]
[tex]d=\sqrt{100}[/tex]
[tex]DE=10\ ft[/tex]
step 4
Find the distance AE
we have
[tex]A(18,20),E(22.10)[/tex]
substitute in the formula
[tex]d=\sqrt{(10-20)^{2}+(22-18)^{2}}[/tex]
[tex]d=\sqrt{(-10)^{2}+(4)^{2}}[/tex]
[tex]d=\sqrt{116}[/tex]
[tex]AE=10.77\ ft[/tex]
step 5
Find out the area of the four walls
To determine the area sum the length sides and multiply by the height of the walls
so
[tex]A=(AB+BC+DE+AE)h[/tex]
substitute the given values
The height of the walls is 10 ft
[tex]A=(14+16+10+10.77)10[/tex]
[tex]A=(50.77)10[/tex]
[tex]A=507.7\ ft^2[/tex]
step 6
Determine the number of gallons needed to paint the four walls
we know that
one gallon of paint is enough to cover 400 square feet
using proportion
[tex]\frac{1}{400}\ \frac{gal}{ft^2}=\frac{x}{507.7}\ \frac{gal}{ft^2}\\\\x=507.7/400\\\\x= 1.27\ gal[/tex]
Round up
[tex]x=2\ gal[/tex]
