What is the surface Area of a triangular prism with 16 inches height. 24 and 60 for base edge and slant height of 20? How would I set this up?
each side face has area 1/2 * its base * slant height.
so add up all those triangles, as well as the area of the base.
To find the surface area of a triangular prism, we need to find the areas of all its faces and add them together.
1. Start by identifying the different faces of the triangular prism:
- The two triangular bases
- The three rectangular faces
2. Calculate the area of one triangular base:
- The area of a triangle can be calculated using the formula: (base * height) / 2.
- In this case, the base edge of the triangular base is 24 inches, and the height is 16 inches. So, the area of one triangular base is (24 * 16) / 2.
3. Calculate the area of the other triangular base:
- Since the bases of a triangular prism are congruent, the area of the other triangular base will be the same as the first one.
4. Calculate the area of each rectangular face:
- The area of a rectangle is given by the formula: length * width.
- In the triangle prism, we have three rectangular faces. For each face:
- One side will be equal to the base edge of the triangular base. So, the length of each face is 24 inches.
- The other side will be equal to the slant height of the triangular base. So, the width of each face is 20 inches.
- Calculate the area of each rectangular face as length * width.
5. Add up the areas of all the faces:
- Add the areas of the two triangular bases calculated in step 2.
- Add the areas of the three rectangular faces calculated in step 4.
Finally, sum up all these areas to find the total surface area of the triangular prism.