The structure shown below will be built for a carnival. The exterior surfaces are going to be painted. What is the total area of the exterior surfaces that need to be painted?

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 square feet.

The area of 4 such rectangular surfaces 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 square feet.

The area of 4 such triangular surfaces square feet.

Step 4:

The total surface area is the sum of all the external surfaces.

The total surface area square feet.

So 760 square feet of surface needs to be painted.