THe area of a trapezoid is 80 units. If its height is 8 units, find the length of its median?
To find the length of the median of a trapezoid, we can use the formula:
Median = (a + b) / 2
where a and b are the lengths of the parallel sides.
In this case, we are given the area of the trapezoid as 80 units and its height as 8 units. Let's assume that the lengths of the parallel sides are a and b.
We know that the area of a trapezoid is given by the formula:
Area = (1/2) * (a + b) * h
Substituting the given values, we have:
80 = (1/2) * (a + b) * 8
Dividing both sides of the equation by 8:
10 = (1/2) * (a + b)
Multiplying both sides of the equation by 2:
20 = a + b
Now, we have a + b = 20.
To find the length of the median, we substitute the value of (a + b) into the formula given earlier:
Median = (a + b) / 2 = 20 / 2 = 10 units
Therefore, the length of the median of the trapezoid is 10 units.
To find the length of the median of a trapezoid, we need to use the formula:
Median = (2 × Area) / Height
Given that the area of the trapezoid is 80 units and its height is 8 units, we can substitute these values into the formula to find the length of the median:
Median = (2 × 80) / 8
Now, let's calculate the length of the median:
Median = 160 / 8
Therefore, the length of the median of the trapezoid is 20 units.
area of trapezoid
= (sum of two parallel sides) x height / 2
80 = (sum of two parallel sides)(8)/ 2
20 = (sum of two parallel sides)
but the median = (sum of two parallel sides)/2
= 10