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

Given the trapezoid:

S=30S=30S=30666999AAABBBCCCDDDEEE

What is the height?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
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

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the trapezoid:

S=30S=30S=30666999AAABBBCCCDDDEEE

What is the height?

2

Step-by-step solution

Formula for the area of a trapezoid:

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

We substitute the data into the formula

9+62×h=30 \frac{9+6}{2}\times h=30

We solve:

152×h=30 \frac{15}{2}\times h=30

712×h=30 7\frac{1}{2}\times h=30

h=30712 h=\frac{30}{7\frac{1}{2}}

h=4 h=4

3

Final Answer

4

Practice Quiz

Test your knowledge with interactive questions

Given the following trapezoid:

AAABBBCCCDDD584

Calculate the area of the trapezoid ABCD.

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