Answer:
![A = 68.8 inches^{2}](https://tex.z-dn.net/?f=A%20%3D%2068.8%20inches%5E%7B2%7D)
Step-by-step explanation:
Given : Jennifer got a box of chocolates. the box is a right triangular prism shaped box. it is 7 in long. and the triangular base measure 2in times 3in times 4in.
a = 2
b=3
c=4
To Find : what is the surface area of the box of chocolates?
Solution: The first thing we should know is the area of the triangular base.
Triangular base area:
![A1 =\sqrt{(s * (s-a) * (s-b) * (s-c)) }](https://tex.z-dn.net/?f=A1%20%3D%5Csqrt%7B%28s%20%2A%20%28s-a%29%20%2A%20%28s-b%29%20%2A%20%28s-c%29%29%20%7D)
Where, s is the semi-meter of the triangle:
![s =\frac{ (a + b + c) }{ 2}](https://tex.z-dn.net/?f=s%20%3D%5Cfrac%7B%20%28a%20%2B%20b%20%2B%20c%29%20%7D%7B%202%7D)
a, b, c: sides of the triangle.
Substituting:
s = (2 + 3 + 4) /2=4.5
![A1 = \sqrt{ (4.5 * (4.5-2) * (4.5-3) * (4.5-4))}](https://tex.z-dn.net/?f=A1%20%3D%20%5Csqrt%7B%20%284.5%20%2A%20%284.5-2%29%20%2A%20%284.5-3%29%20%2A%20%284.5-4%29%29%7D)
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 inches^{2}](https://tex.z-dn.net/?f=A%20%3D%2068.8%20inches%5E%7B2%7D)
Hence the surface area of the box of chocolates is
![A = 68.8 inches^{2}](https://tex.z-dn.net/?f=A%20%3D%2068.8%20inches%5E%7B2%7D)