What is the volume of the given prism? Round the answer to the nearest tenth of a centimeter. The figure is not drawn to scale.
To find the volume of a prism, you multiply the area of the base by the height of the prism.
In this case, the base of the prism is a trapezoid. The formula to find the area of a trapezoid is:
Area = (1/2) * (a + b) * h
where 'a' and 'b' are the lengths of the two parallel sides of the trapezoid, and 'h' is the height of the trapezoid.
First, we need to find the lengths of the two parallel sides of the trapezoid:
Base 1 = 6 cm
Base 2 = 10 cm
Next, we need to find the height of the trapezoid:
Height = 8 cm
Now, we can find the area of the trapezoid:
Area = (1/2) * (6 + 10) * 8
Area = (1/2) * 16 * 8
Area = 64 cm²
Finally, to find the volume of the prism, we multiply the area of the base by the height of the prism:
Volume = 64 cm² * 14 cm
Volume = 896 cm³
Therefore, the volume of the prism is 896 cubic centimeters.