Geometry

Which expression can be used to find the surface area of the triangular prism? 2(1/2 * 3 * 4) + 4 * 2 + 3 * 2 + 5 * 2 What is the surface area of the triangular prism? S.A. = ? ft^2

Step-by-step solution with explanation

Final Answer

Step-by-step solution

1

Identify each part of the expression

The expression has two triangular bases and three rectangular faces. The triangles have base 3 ft and height 4 ft. The rectangles have lengths 4, 3, and 5 ft, each with a width of 2 ft.
2

Calculate the area of the two triangular bases

The area of one triangle is ½ × base × height = ½ × 3 × 4 = 6 sq ft. There are two triangular bases, so we multiply by 2 to get 12 sq ft.
3

Calculate each rectangular face area

Each rectangular face area equals its side length times the prism's depth of 2 ft. We get three rectangles with areas 8, 6, and 10 sq ft.
4

Add all face areas together

Add the two triangle areas and all three rectangle areas. The total surface area is 36 sq ft.

Understanding this problem

Learning Insight

A triangular prism has 5 faces: 2 triangular bases and 3 rectangular sides. The surface area formula always accounts for every face. The two triangles come from the ends of the prism, and the three rectangles 'wrap around' the sides — one for each edge of the triangle.

Quick Tip

To remember the formula, think 'two triangles + three rectangles.' Count the sides of your triangle (3 sides = 3 rectangles). Each rectangle's width is just the depth of the prism.

Common Mistake

Students often forget to include BOTH triangular bases and only add one triangle's area. Always multiply the triangle area by 2 since a prism has two identical ends.