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

Q: How do I know which sides are the bases?

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!

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

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

Q: What if the height isn't given directly?

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.

Q: Can I use this formula for any quadrilateral?

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

Q: What units should my answer have?

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.

Q: How can I remember the trapezoid formula?

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

Trapezoid Area with Parallel Bases

Given the following trapezoid:

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

Understand the problem

Given the following trapezoid:

Calculate the area of the trapezoid ABCD.

Step-by-step solution

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

Given:

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

Apply the trapezoid area formula:

The formula for the area of a trapezoid is:

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

Substitute the values into the formula:

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

Simplify the expression:

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

Calculate:

A = \frac{1}{2} \times 90

Finally, compute the area:

A = 45

Thus, the area of trapezoid ABCD is $45$ .

Final Answer

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

Calculate the area of the trapezoid.

FAQ

Everything you need to know about this question

How do I know which sides are the bases?

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?

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

What if the height isn't given directly?

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?

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?

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?

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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