Question

a monument outside city hall has dimensions as shown in the figure below. if one gallon of paint can cover 271 ft², how many gallons of paint must be bought in order to paint the monument? assume that the base of the monument cannot be painted and that paint can be bought only by the gallon.

Explanation:

Step1: Calculate lateral area of the prism

The prism has 4 rectangular sides. Each rectangle has dimensions 13 ft (width) and 32 ft (height). The lateral - area of the prism $A_{prism}=4\times(13\times32)=4\times416 = 1664$ $ft^{2}$.

Step2: Calculate lateral area of the pyramid

The pyramid has 4 triangular sides. The base of each triangle is 13 ft and the slant - height is 13 ft. The area of a triangle is $A=\frac{1}{2}bh$. So the lateral - area of the pyramid $A_{pyramid}=4\times\frac{1}{2}\times13\times13=4\times\frac{169}{2}=338$ $ft^{2}$.

Step3: Calculate total area to be painted

The total area to be painted $A = A_{prism}+A_{pyramid}=1664 + 338=2002$ $ft^{2}$.

Step4: Calculate number of gallons of paint

Divide the total area by the area covered by one gallon of paint. $n=\frac{2002}{271}\approx7.39$. Since paint can be bought only by the gallon, we need to round up to the next whole number. So $n = 8$.

Answer:

8