if a triangle prism is 8cm and 6cm and 9cm, and 10cm then what is the surface area of the triangle prism
To find the surface area of a triangular prism, you need to calculate the area of each face and then add them all together.
First, calculate the area of the two triangular bases:
Area of a triangle = 1/2 * base * height
Base of the triangle = 8cm
Height of the triangle = 6cm
Area of one triangular base = 1/2 * 8cm * 6cm = 24cm²
Now, we have two triangular bases so we multiply the area of one by two: 2 * 24cm² = 48cm²
Next, calculate the area of the three rectangular faces:
To calculate the area of a rectangle, multiply the length by the width.
There are three rectangular faces in a triangular prism:
1. One face with a length of 8cm and a width of 9cm: 8cm * 9cm = 72cm²
2. One face with a length of 6cm and a width of 9cm: 6cm * 9cm = 54cm²
3. One face with a length of 8cm and a width of 6cm: 8cm * 6cm = 48cm²
Add the areas of the three rectangular faces: 72cm² + 54cm² + 48cm² = 174cm²
Finally, add the area of the two triangular bases and the three rectangular faces together to find the total surface area of the triangular prism:
48cm² (triangular bases) + 174cm² (rectangular faces) = 222cm²
Therefore, the surface area of the triangular prism is 222cm².