Prism measurements: 10 cm 8cm 9cm 6cm
Use the image to answer the question. What is the surface area of the triangular prism? (1 point) square centimeters
To find the surface area of the triangular prism, we need to calculate the area of all six faces and then add them together.
First, we need to find the areas of the two triangular faces. Each triangular face has a base and a height. The two triangular faces are identical, so we can find the area of one and then double it.
The base of the triangle is 8 cm and the height is 6 cm:
Area of one triangle = (1/2) * base * height
Area of one triangle = (1/2) * 8 cm * 6 cm
Area of one triangle = 24 square cm
Now, double the area of one triangle to find the total area of both triangular faces:
Total area of triangular faces = 2 * 24 square cm
Total area of triangular faces = 48 square cm
Next, we need to find the areas of the four rectangular faces. The dimensions of the rectangles are as follows:
- 10 cm by 8 cm (2 faces)
- 10 cm by 9 cm (2 faces)
Area of one rectangular face = length * width
Area of one rectangular face = 10 cm * 8 cm
Area of one rectangular face = 80 square cm
Total area of all four rectangular faces = 4 * 80 square cm
Total area of all four rectangular faces = 320 square cm
Finally, to find the total surface area of the triangular prism, add the areas of all six faces together:
Total surface area = Total area of triangular faces + Total area of rectangular faces
Total surface area = 48 square cm + 320 square cm
Total surface area = 368 square cm
Therefore, the surface area of the triangular prism is 368 square cm.