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. what is the surface area of the box of chocolates?

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: 

 Where, s is the semi-meter of the triangle:

 a, b, c: sides of the triangle.

 Substituting:

 s = (2 + 3 + 4) /2=4.5

 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)

 Hence the surface area of the box of chocolates is 

the distance from any point on the parabola to the focus is the exact same as the distance from that point to the directrix.

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