how to find the height of a trapezoid with median 12 and area 84
A=1/2(h)(a+b)
84=1/2(h)(24)
84=12(h)
h=7
h = height
84 = 12h
84/12 = h
Why did the trapezoid go to therapy? It had trouble finding its height! But don't you worry, I'm here to help.
To find the height of a trapezoid, you first need to know the lengths of its bases. Unfortunately, you only provided the median and area. Are you sure you're not confusing trapezoids with therapists? ๐
To find the height of a trapezoid with a given median and area, you can follow these steps:
Step 1: Recall the formula to find the area of a trapezoid, which is given by the equation:
Area = (1/2) * (sum of bases) * height
Step 2: Substitute the given values into the equation. Let's call the upper base of the trapezoid "a," the lower base "b," and the height "h." The median of a trapezoid is the average of its bases, so in this case, the median is equal to (a + b) / 2. Also, the given area is 84.
We can rewrite the formula as:
84 = (1/2) * (a + b) * h
Step 3: Since the median is given as 12 and is equal to (a + b) / 2, we can substitute 12 for (a + b) / 2:
84 = (1/2) * 12 * h
Simplify the equation:
84 = 6h
Step 4: Solve for h by dividing both sides of the equation by 6:
h = 84 / 6
Simplify further:
h = 14
Therefore, the height of the trapezoid is 14 units.
To find the height of a trapezoid with the median and area given, you can use the formula:
Area = (1/2) * height * (base1 + base2)
In this case, the area is given as 84 and the median is given as 12. Let's label the bases as base1 and base2.
We know that the median of a trapezoid is the average of the two bases. So, we have:
median = (base1 + base2) / 2
Substituting the given median value of 12 into the equation, we get:
12 = (base1 + base2) / 2
Next, we can simplify the formula for the area by substituting the given values of the area (84) and the median (12):
84 = (1/2) * height * (base1 + base2)
Now, let's solve the two equations simultaneously to find the values of base1 and base2. From the first equation, base1 + base2 = 24. We can solve for base1 or base2 by isolating one variable. Let's isolate base1:
base1 = 24 - base2
Substituting this value for base1 in the second equation, we have:
84 = (1/2) * height * (24 - base2 + base2)
Simplifying further:
84 = (1/2) * height * 24
Now, multiply both sides of the equation by 2:
168 = height * 24
Divide both sides by 24:
height = 168 / 24
Finally, calculate the height:
height = 7
Therefore, the height of the trapezoid is 7 units.