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

Trapezoid Area Formula with Height Calculation

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

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area = (b1+b2)2×h \frac{(b_1 + b_2)}{2} \times h where bases are parallel sides
  • Technique: Substitute known values: (6+9)2×h=30 \frac{(6 + 9)}{2} \times h = 30
  • Check: Verify by calculating: 152×4=7.5×4=30 \frac{15}{2} \times 4 = 7.5 \times 4 = 30 ✓

Common Mistakes

Avoid these frequent errors
  • Using non-parallel sides in the formula
    Don't use the slanted sides (legs) as bases in the trapezoid formula = completely wrong area calculation! The legs are not part of the area formula at all. Always identify and use only the two parallel sides as your bases.

Practice Quiz

Test your knowledge with interactive questions

Given the following trapezoid:

AAABBBCCCDDD584

Calculate the area of the trapezoid ABCD.

FAQ

Everything you need to know about this question

How do I identify which sides are the bases in a trapezoid?

+

The bases are the two parallel sides - they never meet even if extended. In this problem, the parallel sides are labeled as 6 and 9. The slanted sides connecting them are called legs.

Why do we divide by 2 in the trapezoid formula?

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Think of a trapezoid as the average of the two parallel sides multiplied by height. (6+9)2=7.5 \frac{(6 + 9)}{2} = 7.5 gives us the average base length!

Can I solve this problem if the area and height were given instead?

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Absolutely! If you knew Area = 30 and height = 4, you could find the sum of the bases: b1+b2=2×304=15 b_1 + b_2 = \frac{2 \times 30}{4} = 15

What if I get a decimal or fraction for the height?

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That's completely normal! Heights can be any positive number. Just make sure your final answer makes sense when you substitute back to check your work.

Is there another way to solve this besides the area formula?

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The trapezoid area formula is the standard method. You could break it into triangles and rectangles, but that's much more complicated and prone to errors.

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