Question

Linda made the sculpture below as part of an art project. The sculpture is made up of a square pyramidand rectangular prism. Linda needs to paint the entire exterior surface, including the bottom. Find theapproximate area she needs to paint. Round to the nearest hundredth.

Answer 1

We need to calculate the surface area of the lateral faces of the square pyramid without the base and the surface area of the rectangular prism without one face

for the lateral faces of the square pyramid

we need to calculate the slant height

$sh=\sqrt[]{3^2+2.5^2}=3.91ft$

then for the lateral area

$LA=4(\frac{(5)\cdot(3.91)}{2})=39.1ft^2$

then for the rectangular prism without the base

$SA=5(5\cdot5)=125ft^2$

The total surface area that she needs to paint is

$\text{TSA}=39.1+125=164.1ft^2$