Question

Height: 10 inches
Base Perimeter: 40 inches
Lateral Surface Area: 400 square inches (^^^this is the total surface area of the sides)

What is the Surface Area of the triangular prism?
(the picture of the shape looks like a pentagon but the rectangle is much longer)

Answer 1

total surface area=side area+base + top

side area given.
base perimeter given

assuming the triangle is regular,then each side of the triangle is 400/(10*3) or 40/3 in length.

area=sqrt(s*(s-a)(s-b)(s-c))

where a=b=c= 40/3, and s is half perimter or 20

areabase=sqrt(20 (20-40/3)^3)
=20 sqrt(2/3)^3=40/3sqrt(2/3)

check that.

then total area=400+2*40/3sqrt2/3 if the above is correct.