Calculate Trapezoid Area: Finding Area of ABCD with Base Lengths 7 and 11

Trapezoid Area with Parallel Bases

Given the following trapezoid:

AAABBBCCCDDD7115

Calculate the area of the trapezoid ABCD.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:04 Let's find the area of the trapezoid.
00:08 We'll use the formula for a trapezoid's area.
00:12 It's: the sum of base A B and base D C, times the height H. Then divide by two.
00:18 Now, we'll put in the values and calculate the area.
00:36 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the following trapezoid:

AAABBBCCCDDD7115

Calculate the area of the trapezoid ABCD.

2

Step-by-step solution

To calculate the area of the trapezoid ABCD, we will follow these steps:

Given:

  • Base AB=7 AB = 7
  • Base CD=11 CD = 11
  • Height =5 = 5

Apply the trapezoid area formula:

The formula for the area of a trapezoid is:

A=12×(Base1+Base2)×Height A = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}

Substitute the values into the formula:

A=12×(7+11)×5 A = \frac{1}{2} \times (7 + 11) \times 5

Simplify the expression:

A=12×18×5 A = \frac{1}{2} \times 18 \times 5

Calculate:

A=12×90 A = \frac{1}{2} \times 90

Finally, compute the area:

A=45 A = 45

Thus, the area of trapezoid ABCD is 45 45 .

3

Final Answer

45

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area equals half times sum of bases times height
  • Technique: Add parallel bases first: 7 + 11 = 18, then multiply
  • Check: Final units are square units and answer seems reasonable ✓

Common Mistakes

Avoid these frequent errors
  • Using wrong bases in the formula
    Don't use the slanted sides as bases = wrong calculation! Only the parallel sides (top and bottom) are bases in a trapezoid. Always identify which sides are parallel before applying the formula.

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?

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The bases are the two parallel sides of the trapezoid. In this problem, AB = 7 and CD = 11 are parallel to each other, so they're the bases!

Why do we multiply by 1/2 in the formula?

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A trapezoid is like the average of two rectangles. The 12 \frac{1}{2} finds the average width, then we multiply by height to get the area.

What if the height isn't given directly?

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Sometimes you need to calculate the height using the Pythagorean theorem or other methods. The height is always the perpendicular distance between the parallel bases.

Can I use this formula for any quadrilateral?

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No! This formula only works for trapezoids because they have exactly one pair of parallel sides. For other shapes, use different formulas.

What units should my answer have?

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Since area measures square units, your answer should have units like cm², m², or just 'square units' if no specific unit is given in the problem.

How can I remember the trapezoid formula?

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Think: 'Half the sum times the height!' You're finding the average of the two bases, then multiplying by how tall the shape is.

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