Question 1181041

PART A

The barn is constructed by the following 2D shapes

Two triangles of height = {{{4}}} and base = {{{20}}}
Area = 2 * (1/2)*4*20) = 80}}}

Two rectangles of length = {{{20}}} and width = {{{15}}}
{{{Area = 2 * 20 * 15 = 600}}}

Two rectangles of length = {{{45}}} and width ={{{ 15}}}
{{{Area = 2 * 45*15 = 1350}}}

One base of length = {{{45}}} and width = {{{15}}}
{{{Area = 45 *15 = 675}}}

Two rectangles on each on one side of the roof. We have the length = {{{45}}} but not the width. We can work out the width by using Pythagoras theorem

{{{w^2 = 4^2 + 10^2}}}
{{{w^2= 16 + 100}}}
{{{w^2= 116}}}
{{{w = sqrt(116) = 10.77}}}

Area of the two rectangles on the roof part is = {{{2*10.77* 45 = 969.33}}}

Total area to paint = {{{969.33+675+1350+600+80 = 3674.33}}}(to the nearest hundreth) ≈ {{{3700}}} 


PART C
one paint can covers {{{57}}} square feet

{{{3700/57=65}}}->need {{{65}}} cans of paint
Total cost of paint ={{{ 65 *23.50 = 1527.50}}}

PART D

The barn is constructed by a cuboid and a rectangular prism

Volume of cuboid {{{V= length *width * height}}}
{{{V= 20*45*15}}}
{{{V=13500}}}

V of triangular prism = Area of cross section × depth
{{{V = ((1/2)*4*20) * 45}}}
{{{V = 1800}}}

Total volume 
= {{{1800 + 13500 = 15300}}}