Question

Lisa's favorite chocolate candies are wrapped in the shape of a triangular prism with shiny gold paper as shown below. If all sides of the package are covered in the gold paper, what is the surface area of the amount that is wrapped?

Answer 1

Surface Area = 150

Explanation:

The surface area of this triangular prism is the sum of area of all the sides.

Surface Area = triangle 1 (with base 8 and height 3) + triangle 2 (same as triangle 1) + lateral surface 1 (with length 7 and width 5 (calculation shown below)) + lateral surface 2 (same as lateral surface 1) + bottom (side not shown with length 7 and width 8)

• Triangle 1 area:
  `(1)/(2)bh=(1)/(2)(8)(3)=12`
• Triangle 2 area:
  `(1)/(2)bh=(1)/(2)(8)(3)=12`
• Lateral surface 1 (rectangle):
  `l*w=(7)(5)=35`
• Lateral surface 2 (rectangle):
  `l*w=(7)(5)=35`
• Bottom surface (rectangle):
  `l*w=(7)(8)=56`

Summing all these gives us the total surface area.

Total surface area =
`12+12+35+35+56=150`

**** The triangle shown is divided into half by the perpendicular line (3cm) to the base. So the base is divided in half (4 cm and 4 cm).

Now, we have a right triangle with one leg 4 cm and another leg 3 cm. How do we get the hypotenuse? We use Pythagorean Theorem. Which is:

`leg^2+leg^2=hypotenuse^2\\3^2+4^2=hypotenuse^2\\25=hypotenuse^2\\hypotenuse=5`

Hence, the side length of the hypotenuse is 5 [used above in the calculation]