Trapezoid Height Calculation: Find h When Area = 30cm² (4cm & 8cm Parallel Sides)

The trapezoid ABCD is shown below.

AB = 4 cm

DC = 8 cm

Area of the trapezoid (S) = 30 cm²

Calculate the height of the trapezoid.

S=30S=30S=30444888AAABBBCCCDDD

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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
00:03 We'll use the formula for calculating the area of a trapezoid
00:06 (Sum of bases(AB+DC) multiplied by height (H)) divided by 2
00:13 We'll substitute appropriate values and solve for the height
00:32 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

The trapezoid ABCD is shown below.

AB = 4 cm

DC = 8 cm

Area of the trapezoid (S) = 30 cm²

Calculate the height of the trapezoid.

S=30S=30S=30444888AAABBBCCCDDD

2

Step-by-step solution

We use the formula to calculate the area: (base+base) times the height divided by 2

We replace the existing data:

S=(AB+CD)×h2 S=\frac{(AB+CD)\times h}{2}

30=(4+8)×h2 30=\frac{(4+8)\times h}{2}

We multiply the equation by 2:

60=(4+8)h 60=(4+8)h

60=12h 60=12h

We divide the two sections by 12:

6012=h \frac{60}{12}=h

5=h 5=h

3

Final Answer

5

Practice Quiz

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Given the following trapezoid:

AAABBBCCCDDD584

Calculate the area of the trapezoid ABCD.

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