Trapezoid Area Formula: Finding Height When Area = 20cm² and Base Sum = 10cm

The trapezoid ABCD has an area equal to 20 cm².

The sum of its bases is 10 cm.

What is the height of the trapezoid?

AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Find the height of the trapezoid
00:04 We'll use the formula for calculating the area of a trapezoid
00:08 (Sum of bases(AB+DC) multiplied by height(H))divided by 2
00:13 We'll substitute appropriate values and solve for H
00:18 Let's isolate H
00:24 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

The trapezoid ABCD has an area equal to 20 cm².

The sum of its bases is 10 cm.

What is the height of the trapezoid?

AAABBBCCCDDD

2

Step-by-step solution

The formula for the area of a trapezoid is given by:

A=12×(b1+b2)×h A = \frac{1}{2} \times (b_1 + b_2) \times h

where A A is the area, b1 b_1 and b2 b_2 are the lengths of the two bases, and h h is the height.

We are given:

  • A=20 cm2 A = 20 \, \text{cm}^2
  • b1+b2=10 cm b_1 + b_2 = 10 \, \text{cm}

We substitute these values into the formula:

20=12×10×h 20 = \frac{1}{2} \times 10 \times h

To find h h , we simplify the equation:

20=5h 20 = 5h

Dividing each side by 5, we get:

h=205 h = \frac{20}{5}

Hence, the height of the trapezoid is:

h=4 cm h = 4 \, \text{cm}

Therefore, the height of the trapezoid is 4 cm.

3

Final Answer

4 cm

Practice Quiz

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Given the following trapezoid:

AAABBBCCCDDD584

Calculate the area of the trapezoid ABCD.

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