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?

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

Step-by-step 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.

cm.

Step 2:

The area of a triangle

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

The area of the triangle square cm.

The area of 2 such triangles square cm.

Step 3:

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

The area of a rectangle

The area of the rectangle with a width of 15 cm .

The area of the rectangle with a width of 10 cm

The area of the rectangle with a width of 11.08 cm

Step 4:

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

The surface area of the prism .

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