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
604.96 cm
528 cm
572.96 cm
532.96 cm
572.96 cm
can you explain
To calculate the surface area of a triangular prism, we need to find the areas of the two triangular bases and the three rectangular faces.
1. Calculate the area of the triangular base:
The formula to find the area of a triangle is 1/2 * base * height.
In this case, the base and height of the triangle are 10cm and 8cm respectively.
Area of the base = 1/2 * 10cm * 8cm = 40 cm^2
2. Calculate the area of the other triangular base:
We know the hypotenuse and one of the legs of the right-angled triangle. We can use these values to find the other leg.
Using the Pythagorean theorem:
12.81^2 = 10^2 + x^2
164.3761 = 100 + x^2
x^2 = 64.3761
x ≈ 8.02 cm
Now we can calculate the area of the second base triangle:
Area of the base = 1/2 * 16cm * 8.02cm = 64.32 cm^2
3. Calculate the area of the three rectangular faces:
Face 1: 8cm * 16cm = 128 cm^2
Face 2: 8cm * 12.81cm = 102.48 cm^2
Face 3: 16cm * 12.81cm = 204.96 cm^2
Now, calculate the total surface area of the triangular prism by adding the areas of the two triangular bases and the three rectangular faces:
Total surface area = 40 cm^2 + 64.32 cm^2 + 128 cm^2 + 102.48 cm^2 + 204.96 cm^2 = 540.76 cm^2
Therefore, the correct answer is 572.96 cm^2.