Calculating Trapezoid Area: Finding the Area of ABCD with 5 and 11 Unit Bases

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

In a trapezoid, the parallel bases are the two sides that never meet, even if extended. In this problem, AB = 5 and CD = 11 are labeled as the parallel sides running horizontally.

Q: Why is the height 4 if it's not labeled in the diagram?

The height is the perpendicular distance between the parallel bases. Sometimes it's given in the problem text or you need to calculate it from other measurements using right triangles.

Q: Wait, the explanation shows height = 4 but gets area = 32. Which is right?

Good catch! There seems to be an inconsistency. If the bases are 5 and 11, and we get area 28 (the correct answer), then: 28 = ½ × (5 + 11) × h, so h = 3.5, not 4.

Q: Can I use this formula for any quadrilateral?

No! This formula only works for trapezoids - quadrilaterals with exactly one pair of parallel sides. For other shapes like rectangles or general quadrilaterals, you need different formulas.

Trapezoid Area with Parallel Base Measurements

Look at the following trapezoid:

Calculate the area of trapezoid ABCD.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:03 Let's find the area of the trapezoid.

00:07 We'll use the formula for the area of a trapezoid.

00:11 Add the lengths of the bases, A B and D C, multiply by the height, H, then divide by two.

00:19 Let's plug in the numbers and solve for the area.

00:37 We'll simplify the terms and find the result.

00:47 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the following trapezoid:

Calculate the area of trapezoid ABCD.

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information.
Step 2: Apply the formula for the area of a trapezoid.
Step 3: Perform the calculations.

Now, let's work through each step:
Step 1: We identify from the problem that $AB = 5$ , $CD = 11$ , and the height $h = 4$ .
Step 2: The formula for the area of a trapezoid is:
$\text{Area} = \frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$ Here, $\text{Base}_1 = 5$ and $\text{Base}_2 = 11$ .
Step 3: Substitute the values into the formula:
$\text{Area} = \frac{1}{2} \times (5 + 11) \times 4 = \frac{1}{2} \times 16 \times 4$ $= \frac{1}{2} \times 64 = 32$

Therefore, the solution to the problem is $\text{Area} = 32$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area = ½ × (base₁ + base₂) × height
Technique: Add parallel bases first: 5 + 11 = 16
Check: Units are squared and result makes geometric sense ✓

Common Mistakes

Avoid these frequent errors

Using wrong height measurement
Don't use the slanted side length as height = wrong area calculation! The slanted sides are NOT the height - they're longer than the perpendicular distance. Always use the perpendicular distance between parallel bases as height.

Practice Quiz

Test your knowledge with interactive questions

Given the following trapezoid:

Calculate the area of the trapezoid ABCD.

FAQ

Everything you need to know about this question

How do I know which sides are the parallel bases?

In a trapezoid, the parallel bases are the two sides that never meet, even if extended. In this problem, AB = 5 and CD = 11 are labeled as the parallel sides running horizontally.

Why is the height 4 if it's not labeled in the diagram?

The height is the perpendicular distance between the parallel bases. Sometimes it's given in the problem text or you need to calculate it from other measurements using right triangles.

Wait, the explanation shows height = 4 but gets area = 32. Which is right?

Good catch! There seems to be an inconsistency. If the bases are 5 and 11, and we get area 28 (the correct answer), then: 28 = ½ × (5 + 11) × h, so h = 3.5, not 4.

Can I use this formula for any quadrilateral?

No! This formula only works for trapezoids - quadrilaterals with exactly one pair of parallel sides. For other shapes like rectangles or general quadrilaterals, you need different formulas.

What if the trapezoid is tilted or oriented differently?

The orientation doesn't matter! Whether the trapezoid is upright, sideways, or tilted, the area formula stays the same. Just identify the parallel bases and perpendicular height.

How do I calculate the area if I only know the coordinates of vertices?

Use the coordinate method: find the lengths of parallel sides using distance formula, then calculate the perpendicular height between them. You can also use the shoelace formula for any polygon.

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