we know that
The surface area of a square pyramid is given by the formula
[tex]SA=B+LA[/tex]where
B is the area of the square base
LA is the lateral area (area of the four triangular faces)
step 1
Find out the area of the square base B
[tex]\begin{gathered} B=96^2 \\ B=9,216\text{ m}^2 \end{gathered}[/tex]step 2
Find out the area of one triangular face
the area of one triangular face is given by the formula
[tex]A=\frac{1}{2}*b*h[/tex]where
b=96 m
h=?
Applying the Pythagorean Theorem, find out the value of h
[tex]h^2=H^2+(\frac{b}{2})^2[/tex]where
H=220 m (height of the building)
b/2=96/2=48 m
substitute
[tex]\begin{gathered} h^2=220^2+(48)^2 \\ h^2=50,704 \\ h=225.18\text{ m} \end{gathered}[/tex]substitute
[tex]\begin{gathered} A=\frac{1}{2}*96*225.18 \\ A=10,808.64\text{ m}^2 \end{gathered}[/tex]Multiply by 4 to obtain the Lateral Area
[tex]\begin{gathered} LA=4*10,808.64 \\ LA=43,234.56\text{ m}^2 \end{gathered}[/tex]The surface area of the building is equal to
[tex]\begin{gathered} SA=9,216+43,234.56 \\ SA=52,450.56\text{ m}^2 \end{gathered}[/tex]step 3
we know that
one gallon of cleaning solution -----> for every 250 square meters of surface
Applying proportion
1/250=x/52,450.56
solve for x
x=52,450.56/250
x=210 gallons
see the figure below to better understand the calculation to obtain the value of
h (the height of each triangular face)
