The surface area of the prism is 161 square feet.
Step-by-step explanation:
Step 1:
In order to calculate the surface area of the entire prism, we must calculate the individual areas of all the sides.
The triangular prism consists of 2 triangles and 3 rectangles.
Step 2:
The area of a triangle is half the product of the base length and its height.
The triangles have a base length of 5 feet and a height of 5 feet.
The area of 2 triangles = [tex]2(\frac{1}{2} (5)(5)) = 25.[/tex]
Step 3:
The area of a rectangle is the product of its length and width.
There a 3 rectangles out of which 2 are similar.
The similar rectangles have lengths of 8 feet and widths of 5 feet.
The area of 2 similar rectangles[tex]= 2 (8)(5) = 80.[/tex]
The third rectangle has a length of 8 feet and a width of 7 feet.
The area of the third rectangle[tex]= (8)(7) = 56.[/tex]
Step 4:
The surface area of the prism = The area of the 2 triangles + The area of the 3 rectangles.
The surface area of the prism [tex]= 25 + 80 + 56 = 161.[/tex]
The surface area of the prism is 161 square feet.
