Christian Christian collects model cars and planes he has a display showcase of all of his collectors items softest real world problem to find the surface of the area displayed showcase if it is the shape of a triangular prism with the following dimensions height equals nine base equals 17 side 110 side to 12 side 317 and length 10
To find the surface area of the triangular prism showcase, you would first need to calculate the area of each individual face.
The formula to calculate the surface area of a triangular prism is:
Surface Area = 2*(base area) + (lateral area)
Base Area:
- The base of the triangular prism is a triangle with a base of 17 and height of 9.
- The formula to calculate the area of a triangle is:
Area = 1/2 * base * height
Area = 1/2 * 17 * 9
Area = 1/2 * 153
Area = 76.5
Lateral Area:
- The lateral faces of the triangular prism are rectangles.
- To calculate the area of each rectangle, you need to multiply the length by the height.
- The formula to calculate the lateral area of a prism is:
Lateral Area = 2*(side1*height) + 2*(side2*height) + 2*(side3*height)
Lateral Area = 2*(110*9) + 2*(12*9) + 2*(317*9)
Lateral Area = 1980 + 216 + 5718
Lateral Area = 7914
Now, you can calculate the total surface area of the triangular prism showcase by adding the base area and lateral area together:
Surface Area = 2*(76.5) + 7914
Surface Area = 153 + 7914
Surface Area = 8067
Therefore, the surface area of Christian's triangular prism showcase is 8067 square units.