Area of trapezoid is 80 square units, height is 8 units. What is the lenght of median ?
since the area is the height times the median
80 = 8m
. . .
12
To find the length of the median of a trapezoid, we need to know the lengths of the two bases. However, in this case, we only have the area and the height.
Let's denote the lengths of the two bases as 'b1' and 'b2'. The formula to calculate the area of a trapezoid is:
Area = (b1 + b2) * height / 2
Given that the area is 80 square units and the height is 8 units, we can rewrite the formula as:
80 = (b1 + b2) * 8 / 2
Simplifying further:
80 = (b1 + b2) * 4
Next, we need to use an additional piece of information about a trapezoid. The median of a trapezoid is defined as the average of the two bases. This can be represented by the equation:
Median = (b1 + b2) / 2
By rearranging this equation, we have:
b1 + b2 = 2 * Median
Now, let's substitute this value back into the area formula:
80 = (2 * Median) * 4
Simplifying further:
80 = 8 * Median
Dividing both sides of the equation by 8:
10 = Median
Therefore, the length of the median of the trapezoid is 10 units.