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Use a conversion factor to convert from yards to feet. The area of a trapezoid is one half of the product of its height and the sum of its bases.
648ft^2
We are told that a trapezoid has base lengths of 5 and 7 yards and a height of 12 yards. Let's see the diagram!
Before we substitute these two values into the formula for the area of a trapezoid, let's convert the yards into feet. Converting between yards and feet will involve using a conversion factor.
| Yards | Conversion | Feet | |
|---|---|---|---|
| Bottom Base | 7 | 7* 3 | 21 |
| Top Base | 5 | 5* 3 | 15 |
| Height | 12 | 12* 3 | 36 |
We found that the bottom base of the trapezoid is 21 feet, the top base is 15 feet, and the height is 36 feet. Now we can substitute these values into the formula for the area of a trapezoid. Let's do it!
Substitute values
Add terms
Multiply
a/c* b = a* b/c
Calculate quotient
The area of the trapezoid is 648 square feet.
Additionally, we have a theorem that tells us about the midsegment of a trapezoid.
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Trapezoid Midsegment Theorem |
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The midsegment of a trapezoid is parallel to each base and it has a measure of one half the sum of the lengths of the bases. |