Which of the following describes a valid method for calculating the surface area of a triangular prism?
1. Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
2.Decompose the triangular prism into three triangles and two rectangles. Find the sum of the area of all five shapes.
3.Decompose the triangular prism into two triangles and three rectangles. Find the sum of twice the area of one triangle and three times the area of one rectangle.
4.Decompose the triangular prism into three triangles and two rectangles. Find the sum of three times the area of one triangle and twice the area of one rectangle.
1. Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
The correct answer is option 1: Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
The valid method for calculating the surface area of a triangular prism is described in option 1. You can decompose the prism into two triangles and three rectangles. Then, find the area of each shape and sum them all up to get the total surface area of the prism.
To calculate the surface area using this method, you would follow these steps:
1. Identify the base of the triangular prism, which is one of the triangle faces.
2. Calculate the area of the base triangle using the formula: Area = (base x height) / 2.
3. Identify the lateral faces of the prism, which are the remaining two triangles.
4. Calculate the area of each lateral triangle using the same formula: Area = (base x height) / 2.
5. Identify the remaining three faces of the prism, which are rectangles.
6. Calculate the area of each rectangle using the formula: Area = length x width.
7. Sum up the areas of all five shapes to find the total surface area of the prism.