What is the surface area of a triangular prism with a height of 8cm, length of 10cm, width of 16cm, and a hypotenuse of 12.81cm
To calculate the surface area of a triangular prism, we need to find the area of the two triangular bases and the three rectangular sides.
1. Area of the triangular base:
The area of a triangle can be calculated using the formula A = 1/2 * base * height.
The base and height of the triangle can be found using the length and width of the prism.
base = 10 cm
height = 16 cm
Area = 1/2 * 10 cm * 16 cm
Area = 80 cm²
Since there are two triangular bases, the total area of the bases is:
2 * 80 cm² = 160 cm²
2. Area of the rectangular sides:
The rectangular sides can be considered as rectangles with dimensions equal to the height of the prism (8 cm) and the hypotenuse length (12.81 cm).
There are three sides, so the area of all three sides is:
3 * 8 cm * 12.81 cm = 308.16 cm²
3. Total Surface Area:
Adding the areas of the two triangular bases and the three rectangular sides, we get:
Total Surface Area = 160 cm² + 308.16 cm²
Total Surface Area = 468.16 cm²
Therefore, the surface area of the triangular prism is 468.16 cm².