The area of a trapezoid is 80 square units. If its height is 8 units, find the length of its median.
10 units
To find the length of the median of a trapezoid, you need to know the lengths of its bases. In this case, we are given the height of the trapezoid but not the lengths of the bases.
However, since we also know the area of the trapezoid, we can use the formula for the area of a trapezoid to find a relationship between the lengths of the bases.
The formula for the area of a trapezoid is:
Area = (1/2) * (sum of bases) * height
In this case, the area is given as 80 square units, and the height is given as 8 units. So we have:
80 = (1/2) * (sum of bases) * 8
Simplifying the equation, we get:
80 = 4 * (sum of bases)
To find the length of the median, we need the sum of the bases. Dividing both sides of the equation by 4, we get:
20 = sum of bases
Now let's assume the lengths of the bases are b1 and b2. Since the median of a trapezoid is the average of the lengths of its bases, we can calculate it by dividing the sum of the bases by 2:
Median = (b1 + b2) / 2
Substituting the sum of the bases we found earlier, we have:
Median = (20) / 2
Median = 10 units
Therefore, the length of the median of the trapezoid is 10 units.