To find the surface area you will need to find the area of all 5 surfaces (faces) on the prism. On a triangular prism there are 2 triangular faces and 3 rectangular faces. All 3 rectangular faces are the same and the 2 triangular faces are also the same.
To find the area of the triangular faces, you will use the formula for finding the area of a triangle:
A = 1/2bh 1/2 x 10 x 8.7 A = 43.5 in^2
To find the area of the rectangular faces, you will use the formula for finding the area of a rectangle:
A = bh 10 x 3 A = 30 in ^2
30 + 30 + 30 + 43.5 + 43.5 = 177
The minimum amount of wrapping paper needed for the gift is 177 square inches.
Euler's formula states that the sum of the number of faces (F) and the number of vertices (V) of a polyhedra is equivalent to two more than the number of its edges (E) , that is
