Calculate Trapezoid Area: Finding Area of ABCD with Bases 5 and 10

Q: Which sides are the bases in a trapezoid?

The bases are the two parallel sides. In this problem, AB (length 5) and DC (length 10) are parallel to each other, so they're the bases. The other two sides are the legs.

Q: How do I identify the height from the diagram?

The height is the perpendicular distance between the parallel bases. Look for the dashed line or right angle symbol - here it's the vertical line showing height = 4.

Q: Why do we take half of the sum of the bases?

Think of it as finding the average of the two bases! A trapezoid is like a rectangle with an average width of $ \frac{5+10}{2} = 7.5 $, so area = 7.5 × 4 = 30.

Q: What if the trapezoid is rotated or flipped?

The formula stays the same! Just identify which two sides are parallel (the bases) and measure the perpendicular distance between them (the height). Orientation doesn't matter.

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 quadrilaterals, you need different methods.

Trapezoid Area with Parallel Base Measurements

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

00:00 Calculate the area of the trapezoid

00:03 We'll use the formula for calculating trapezoid area

00:07 (Sum of bases(AB+DC) multiplied by height(H)) divided by 2

00:16 Let's substitute appropriate values and solve for the area

00:27 Let's factor 4 and simplify

00:38 And this is the solution to the question

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 solve this problem, we'll calculate the area of trapezoid ABCD using the appropriate formula.

The formula for the area $A$ of a trapezoid is given by:

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

Substituting the given values into the formula, we have:

$A = \frac{1}{2} \times (5 + 10) \times 4$

First, calculate the sum of the bases:

$5 + 10 = 15$

Multiply by the height, and then take half:

$A = \frac{1}{2} \times 15 \times 4 = \frac{1}{2} \times 60 = 30$

Therefore, the area of the trapezoid ABCD is 30 square units.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals half the sum of bases times height
Calculation: $\frac{1}{2} \times (5 + 10) \times 4 = 30$
Verification: Check that both parallel sides are bases and height is perpendicular ✓

Common Mistakes

Avoid these frequent errors

Using the wrong formula or forgetting to multiply by 1/2
Don't just multiply base times height like a rectangle = 5 × 4 = 20 or 10 × 4 = 40! A trapezoid needs the average of both bases. Always use $\frac{1}{2} \times (\text{Base}_1 + \text{Base}_2) \times \text{Height}$ .

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

Which sides are the bases in a trapezoid?

The bases are the two parallel sides. In this problem, AB (length 5) and DC (length 10) are parallel to each other, so they're the bases. The other two sides are the legs.

How do I identify the height from the diagram?

The height is the perpendicular distance between the parallel bases. Look for the dashed line or right angle symbol - here it's the vertical line showing height = 4.

Why do we take half of the sum of the bases?

Think of it as finding the average of the two bases! A trapezoid is like a rectangle with an average width of $\frac{5+10}{2} = 7.5$ , so area = 7.5 × 4 = 30.

What if the trapezoid is rotated or flipped?

The formula stays the same! Just identify which two sides are parallel (the bases) and measure the perpendicular distance between them (the height). Orientation doesn't matter.

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 quadrilaterals, you need different methods.

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Calculate Trapezoid Area: Finding Area of ABCD with Bases 5 and 10

Trapezoid Area with Parallel Base Measurements

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Which sides are the bases in a trapezoid?

How do I identify the height from the diagram?

Why do we take half of the sum of the bases?

What if the trapezoid is rotated or flipped?

Can I use this formula for any quadrilateral?

🌟 Unlock Your Math Potential

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