Calculate Trapezoid Height: Given Area 30 and Parallel Sides 6 and 9

Question

Given the trapezoid:

What is the height?

00:00 What is the height of trapezoid BE?

00:03 Let's mark the side lengths according to the given data

00:08 Let's mark the trapezoid area according to the given data

00:14 We'll use the formula for calculating trapezoid area

00:19 (Trapezoid height multiplied by the sum of bases) divided by 2

00:23 Let's mark the area of ABCD according to the given data

00:28 Let's mark the values of sides (AB,DC) according to the given data

00:37 Always solve parentheses before multiplication

00:42 Multiply each fraction by the denominator of the other side (common denominator)

00:53 Let's continue solving according to the proper order of operations

01:00 Divide by 15 in order to isolate BE

01:07 Reduce the 15 and we'll be left with just BE on one side

01:12 This is the height of the trapezoid and the answer to the question

Formula for the area of a trapezoid:

$\frac{(base+base)}{2}\times altura$

We substitute the data into the formula

$\frac{9+6}{2}\times h=30$

We solve:

$\frac{15}{2}\times h=30$

$7\frac{1}{2}\times h=30$

$h=\frac{30}{7\frac{1}{2}}$

$h=4$