Surface Area of Triangular Prisms Quick Check3 of 53 of 5 ItemsQuestionUse 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)Responses280 square centimeters280 square centimeters180 square centimeters180 square centimeters260 square centimeters260 square centimeters320 square centimeters
To find the surface area of the triangular prism, we need to find the areas of the two triangular faces and three rectangular faces.
1. Triangular faces:
Area of one triangular face = (1/2) * base * height
Area of one triangular face = (1/2) * 10 cm * 8 cm = 40 square cm
Since there are two triangular faces, the total area of the triangular faces = 2 * 40 square cm = 80 square cm
2. Rectangular faces:
- The two faces parallel to the base are rectangular, each with an area of base * height = 6 cm * 8 cm = 48 square cm.
- The face opposite the base is a rectangle that is not visible in the image, but its area is the same as the area of the one to the left.
Therefore, the total area of the rectangular faces = 2 * 48 square cm = 96 square cm
Adding the areas of the triangular faces and the rectangular faces together:
Total surface area = 80 square cm (triangular faces) + 96 square cm (rectangular faces) = 176 square cm
Therefore, the surface area of the triangular prism is 176 square centimeters.