Calculate Trapezoid Area: 7-Unit Base with Heights 2 and 9

Trapezoid Area with Base Identification

What is the area of the trapezoid in the figure?

222999777AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the area of the trapezoid
00:03 Let's use the formula for calculating the area of a trapezoid
00:07 (Sum of bases(AB+DC) multiplied by height(H)) divided by 2
00:18 Let's substitute appropriate values according to the given data and solve for the area
00:25 In this case, the height is side AD
00:45 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the area of the trapezoid in the figure?

222999777AAABBBCCCDDD

2

Step-by-step solution

We use the formula: (base + base) multiplied by height divided by 2:

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

Keep in mind that AD is the height of a trapezoid:

We insert the existing data into the formula:

S=(2+9)×72 S=\frac{(2+9)\times7}{2}

S=11×72=772=38.5 S=\frac{11\times7}{2}=\frac{77}{2}=38.5

3

Final Answer

38.5 38.5 cm².

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area equals sum of parallel bases times height divided by 2
  • Technique: Identify parallel sides: AB = 2 and DC = 9 are the bases
  • Check: Verify formula gives (2+9)×72=38.5 \frac{(2+9) \times 7}{2} = 38.5 ✓

Common Mistakes

Avoid these frequent errors
  • Using wrong sides as bases in the formula
    Don't use AD or BC as bases in the trapezoid formula = wrong answer like 16 or 23! These are the heights or slanted sides, not the parallel bases. Always identify which sides are parallel first - here AB = 2 and DC = 9 are the 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 know which sides are the bases of a trapezoid?

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The bases are the two parallel sides! In this figure, the horizontal sides AB = 2 and DC = 9 are parallel to each other, so they're your bases.

What's the difference between height and the slanted side?

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The height is the perpendicular distance between the parallel bases (here it's 7). The slanted side BC connects the bases but isn't used in the area formula.

Why do we divide by 2 in the trapezoid formula?

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Think of it as the average of the two bases times the height! 2+92=5.5 \frac{2+9}{2} = 5.5 is the average base length, then multiply by height 7.

Can I use this formula for any quadrilateral?

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No! This formula only works for trapezoids (quadrilaterals with exactly one pair of parallel sides). For other shapes, you need different formulas.

What if the trapezoid is rotated or tilted?

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The formula still works! Just identify the parallel sides (bases) and find the perpendicular distance between them (height), regardless of orientation.

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