Given:
The rectangular prism has a length of 25 feet, a width of 10 feet and a height 55 feet.
The triangular prism has a base length of 25 feet, a height of 8 feet, and a prism height of 55 feet.
To find:
The total area to be painted.
Solution:
There are 4 external surfaces for the rectangular prism and 4 external surfaces for the triangular prism.
The rectangular prism has 4 rectangles out which there are 2 sets of similar rectangles.
There are two rectangles with lengths of 25 feet and widths of 10 feet while the other two rectangles have lengths of 55 feet and widths of 10 feet.
The area of a rectangle with a length of 25 feet and a width of 10 feet [tex]= 25(10)= 250[/tex] square ft.
The area of two such rectangles [tex]= 2(250) = 500[/tex] square feet.
The area of a rectangle with a length of 55 feet and a width of 10 feet [tex]= 55(10)= 550[/tex] square feet.
The area of two such rectangles [tex]= 2(550) = 1100[/tex] square feet.
The triangular prism has 2 triangles and 2 rectangles.
The triangles have base lengths of 25 feet and heights of 8 feet while the rectangles have lengths of 55 feet and heights of 14.8 feet.
The area of a triangle with a base length of 25 feet and a height of 8 feet [tex]= \frac{1}{2}(25)(8)= 100[/tex] square feet.
The area of two such triangles [tex]=2(100)= 200[/tex] square feet.
The area of a rectangle with a length of 55 feet and a width of 14.8 feet [tex]= 55(14.8)= 814[/tex] square feet.
The area of two such rectangles [tex]= 2(814) = 1628[/tex] square feet.
The total area to be painted [tex]=500+1100+200+1628 = 3128[/tex] square feet.
So an area of 3128 square feet is to be painted.
