760 square feet of surface needs to be painted.
Step-by-step explanation:
Step 1:
To determine the total area of all the exterior surfaces, we need to determine how many external surfaces there are.
For this structure, there are 4 rectangular surfaces and 4 triangular surfaces. The base of the shape will not be painted.
Step 2:
The rectangles have lengths of 10 feet and widths of 12.5 feet.
The area of a rectangle is the product of its length and its width.
The area of a rectangular surface [tex]= (10)(12.5) = 125[/tex] square feet.
The area of 4 such rectangular surfaces [tex]= 4(125) = 500[/tex] square feet.
Step 3:
The triangles have base lengths of 10 feet and heights of 13 feet.
The area of a triangle is half the product of its base length and its height.
The area of a triangular surface [tex]=\frac{1}{2} (10)(13) = 65[/tex] square feet.
The area of 4 such triangular surfaces [tex]= 4(65) = 260[/tex] square feet.
Step 4:
The total surface area is the sum of all the external surfaces.
The total surface area [tex]= 500 + 260 = 760[/tex] square feet.
So 760 square feet of surface needs to be painted.
