Answer:
Surface area = 5796 square inches
Explanation:
One formula for surface area of a triangular prism we can use is:
SA = B + Pl, where
- SA is the surface area in square units,
- B is the area of the triangle multiplied by 2 b/c there's 2 triangles,
- and l is the length of the prism
Step 1: We know that the formula for area of a triangle is A = 1/2bh, where
- b is the base,
- and h is the height
Because the base of the triangle is 36 in. and the height is 38 in., we can now find B (aka combined area of both triangles):
B = 2 * (0.5 * 36 * 38)
B = 2 * 684
B = 1368 square in.
Step 2: The formula for perimeter of a triangle is
P = s1 + s2 + s3, where
- s1, s2, and s3 are the sides of the triangles
Since this is an equilateral triangle where all sides measure 36 in., we can find the perimeter by multiplying 36 by 3:
P = 108 in.
Step 3: l = 41 in. Since we now know that B = 1368, P = 108, and l = 41, we can find the surface area by plugging everything into the formula:
SA = B + Pl
SA = 1386 + 108 * 41
SA = 1386 + 4428
SA = 5796 square in.