Which of the following describes a valid method for calculating the surface area of a triangular prism?(1 point)
Responses
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of one triangle and three times the area of one rectangle.
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of one triangle and three times the area of one rectangle.
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.
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.
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of all five shapes.
Decompose the triangular prism into three triangles and two rectangles. Find the sum of the area of all five shapes.
Decompose the triangular prism into two triangles and three rectangles. Find the sum of the area of one triangle and three times the area of one rectangle.
Use the image to answer the question.
An illustration shows a triangular prism. The front triangular face is visible. The left rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. All sides of the triangle measure 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 8 centimeters. The width of the rectangular face measures 6 centimeters.
Solve for the surface area of the triangular prism.
(1 point)
To calculate the surface area of a triangular prism, you first need to find the areas of each face.
1. The triangular face: The formula for the area of a triangle is A = 1/2 * base * height. In this case, the base is the 10 cm side of the triangle and the height is the perpendicular height of 8 cm. So, the area of the triangular face is A = 1/2 * 10 cm * 8 cm = 40 square centimeters.
2. The rectangular face: The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is the 10 cm side of the triangle and the width is given as 6 cm. Therefore, the area of the rectangular face is A = 10 cm * 6 cm = 60 square centimeters.
3. The other rectangular face (not visible in the image) will have the same area as calculated for the visible rectangular face (since their dimensions are the same).
Now, to find the total surface area of the triangular prism, you add the areas of all the faces together:
Total Surface Area = 40 sq cm (triangle) + 60 sq cm (visible rectangle) + 60 sq cm (other rectangle) = 160 sq cm
Therefore, the surface area of the triangular prism is 160 square centimeters.