I have a trapezoid where the height is 16m, the base is 20m,and the area is 224m squared. what is the legnth of the other base
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The area is equal to the height times the average of the bases. Since the Area is 224 and the height is 16, the average of the bases must be 14. (16 * 14 = 224). Since the average of the bases must be 14, and one is 20, then the other must be 8.
To find the length of the other base of the trapezoid, you can use the formula for the area of a trapezoid.
The formula for the area of a trapezoid is:
Area = (1/2) * (b1 + b2) * h
Where b1 and b2 are the lengths of the bases of the trapezoid, and h is the height.
In this case, you are given the following information:
- Height (h) = 16m
- Base (b1) = 20m
- Area = 224m^2
You are looking to find the length of the other base (b2).
Using the formula for the area of a trapezoid, you can rearrange the formula to solve for b2:
224 = (1/2) * (20 + b2) * 16
First, simplify the equation:
224 = 10 + (1/2) * b2 * 16
Multiply both sides of the equation by 2 to eliminate the fraction:
448 = 20 + b2 * 16
Subtract 20 from both sides of the equation:
428 = b2 * 16
Divide both sides of the equation by 16:
b2 = 428/16
Simplify the fraction:
b2 = 26.75
Therefore, the length of the other base is approximately 26.75 meters.