To find the surface area of the triangular prism, we need to find the areas of all the individual faces and then add them up.
1. Area of the front triangular face:
The area of a triangle can be found using the formula A = 1/2 * base * height.
In this case, the base of the triangle is 10 cm and the height is 8 cm.
So, the area of the front triangular face is 1/2 * 10 * 8 = 40 square cm.
2. Area of the back triangular face:
Since the back triangular face is congruent to the front triangular face, its area is also 40 square cm.
3. Area of the left rectangular face:
The area of a rectangle can be found using the formula A = length * width.
In this case, the length is the height of the prism which is also 8 cm, and the width is 6 cm.
So, the area of the left rectangular face is 8 * 6 = 48 square cm.
4. Area of the right rectangular face:
Since the right rectangular face is congruent to the left rectangular face, its area is also 48 square cm.
5. Area of the top face:
The top face is a rectangle with dimensions 10 cm by 6 cm, so its area is 10 * 6 = 60 square cm.
6. Area of the bottom face:
The bottom face is also a rectangle with dimensions 10 cm by 6 cm, so its area is 10 * 6 = 60 square cm.
Now, add up all the individual face areas to get the total surface area of the prism:
40 (front triangular face) + 40 (back triangular face) + 48 (left rectangular face) + 48 (right rectangular face) + 60 (top face) + 60 (bottom face) = 296 square cm
Therefore, the surface area of the triangular prism is 296 square cm.
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.
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1 answer