The volume of a trapezoidal prism can be calculated using a straightforward formula. The volume is determined by multiplying the area of the trapezoidal base by the height (or length) of the prism. The formula is as follows:
Volume = Area of the base × Height
To find the area of the trapezoidal base, you can use the formula for the area of a trapezoid:
Area = (1/2) × (b1 + b2) × h
Where b1 is the length of the first base, b2 is the length of the second base, and h is the height of the trapezoid (the distance between the two bases).
So, putting it all together, you first need to calculate the area of the trapezoidal base using the trapezoid formula and then multiply that area by the height of the prism to get the total volume.
For example, if you have a trapezoidal prism with bases of lengths 5 units and 7 units, a height of 4 units for the trapezoid, and a height of the prism of 10 units, you would calculate it like this:
1. Find the area of the base:
Area = (1/2) × (5 + 7) × 4 = (1/2) × 12 × 4 = 24 square units
2. Now find the volume:
Volume = Area × Height = 24 × 10 = 240 cubic units