Question

Jennifer got a box of chocolates. The box is a right triangular prism shaped box. It is 7 inches long, and the triangular base measures 2 in x 3 in x 4 in. What is the surface area of the box of chocolates?(show work)

Answer 1

The first thing we should know is the area of the triangular base.
Triangular base area:
A1 = root (s * (s-a) * (s-b) * (s-c))
Where, s is the semi-meter of the triangle:
s = (a + b + c) / 2
a, b, c: sides of the triangle.
Substituting:
s = (2 + 3 + 4) /2=4.5
A1 = root (4.5 * (4.5-2) * (4.5-3) * (4.5-4))
A1 = 2.90
Then, you must know the area of each rectangle associated with each side of the triangular base.
Rectangle area 1:
Ar1 = (a) * (l)
Ar1 = (2) * (7)
Ar1 = 14
Rectangular area 2:
Ar2 = (b) * (l)
Ar2 = (3) * (7)
Ar2 = 21
Rectangular area 3:
Ar3 = (a) * (l)
Ar3 = (4) * (7)
Ar3 = 28
Finally the surface area is:
A = Ar1 + Ar2 + Ar3 + 2 * A1
A = (14) + (21) + (28) + 2 * (2.90)
A = 68.8 in ^ 2
answer:
the surface area of the box of chocolates is
A = 68.8 in ^ 2