Question

Joseph Is wrapping a gift shaped like a triangular prism.

15 cm
12 cm
10 cm
What is the least amount of wrapping paper Joseph needs to wrap the gift, in
square centimeters?

Answer 1

Joseph will need at least d. 516.3 square cm of wrapping paper to wrap the triangular prism.

Explanation:

Step 1:

To determine the amount of paper required to wrap the triangular prism, we need to determine the surface area of the entire prism.

The prism consists of 2 similar rectangles and 3 rectangles.

According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Assume the unknown side is x cm long.

`15^(2) = 10^(2) +x^(2) , x^(2) = 225-100=125.`

`x=11.08` cm.

Step 2:

The area of a triangle
`= (1)/(2) (b)(h).`

Here the triangles have a base length of 10 cm and a height of 11.08 cm.

The area of the triangle
`= (1)/(2) (10)(11.08)= 55.4` square cm.

The area of 2 such triangles
`= 2(55.4) = 110.8` square cm.

Step 3:

There are three rectangles with a common length i.e. 12 cm.

The area of a rectangle
`= (l)(w).`

The area of the rectangle with a width of 15 cm
`= (12)(15) = 180`.

The area of the rectangle with a width of 10 cm
`= (12)(10) = 120.`

The area of the rectangle with a width of 11.08 cm
`= (12)(11.08) = 132.96.`

Step 4:

The surface area of the entire prism is the sum of all 5 side areas.

The surface area of the prism
`= 110.8+180+120+132.96 = 543.76`.

This is closest to option d which is 516.3 square cm.