A math teacher keeps her wall-sized graph paper in a box shaped like a triangular prism. The triangular face of the prism has a base of 21 cm and a height of 16 cm. The length of the entire box is 150 cm.
Which of the following is the volume of the box?
To find the volume of the triangular prism box, we need to use the formula for the volume of a prism, which is:
Volume = base area x height
First, let's find the base area of the triangular face of the prism. The formula for the area of a triangle is:
Area = 1/2 x base x height
Plugging in the values given:
Area = 1/2 x 21 cm x 16 cm
Area = 1/2 x 336 cm²
Area = 168 cm²
Now, we can find the volume of the box:
Volume = base area x length
Volume = 168 cm² x 150 cm
Volume = 25,200 cm³
Therefore, the volume of the triangular prism box is 25,200 cm³.