Trapezoid Area 1.375 cm²: Find the Red Side Length

Q: Why is the trapezoid formula different from rectangle?

A trapezoid has two different parallel sides, so we need to find their average length first. The formula $ \frac{(a+b)}{2} $ gives us the average base length, then we multiply by height.

Q: Which sides are the parallel ones in this problem?

The top side AB (red line) and bottom side DC are parallel. The height of 0.5 cm is the perpendicular distance between these parallel sides.

Q: Can I solve this by rearranging the formula first?

Yes! You can rearrange to get: $ AB = \frac{2 \times Area}{h} - DC $. This gives you $ AB = \frac{2 \times 1.375}{0.5} - 4 = 5.5 - 4 = 1.5 $ cm.

Q: What if I mixed up which measurement is the height?

The height is always the perpendicular distance between the parallel sides, not the slanted sides. In this diagram, the 0.5 cm is clearly marked as the vertical distance.

Q: How do I check my answer makes sense?

The red side AB = 1.5 cm should be shorter than the bottom side DC = 4 cm for this trapezoid shape. Also, substitute back: $ \frac{(1.5+4)}{2} \times 0.5 = 1.375 $ ✓

Trapezoid Area Formula with Unknown Side

The area of the trapezoid in the diagram is 1.375 cm².

Work out the length of the side marked in red.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:09 Let's find A B.

00:12 We'll use the trapezoid area formula.

00:16 Add the lengths of the bases, A B and D C, multiply by the height, H, and then divide by 2.

00:25 Now, substitute the given values to solve for A B.

00:38 Multiply both sides by 2 to clear the fraction.

00:54 Next, multiply by the reciprocal.

01:03 Isolate A B to find its value.

01:14 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

The area of the trapezoid in the diagram is 1.375 cm².

Work out the length of the side marked in red.

Step-by-step solution

The area of the trapezoid will be equal to: $S=\frac{(AB+DC)}{2}\times h$

We insert the available data into the formula:

$1.375=\frac{AB+4}{2}\times0.5$

We then multiply by 2 in order to remove the fraction:

Lastly we again multiply by 2:

$5.5=AB+4$

$5.5-4=AB$

$1.5=AB$

Final Answer

$1.5$ cm

Key Points to Remember

Essential concepts to master this topic

Formula: Area = $\frac{(a+b)}{2} \times h$ where a, b are parallel sides
Technique: Substitute known values: $1.375 = \frac{(AB+4)}{2} \times 0.5$
Check: Verify: $\frac{(1.5+4)}{2} \times 0.5 = 1.375$ ✓

Common Mistakes

Avoid these frequent errors

Forgetting to divide by 2 in trapezoid formula
Don't use Area = (a+b) × h = wrong result twice as large! The trapezoid formula requires averaging the parallel sides first. Always use Area = $\frac{(a+b)}{2} \times h$ with the division by 2.

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

Why is the trapezoid formula different from rectangle?

A trapezoid has two different parallel sides, so we need to find their average length first. The formula $\frac{(a+b)}{2}$ gives us the average base length, then we multiply by height.

Which sides are the parallel ones in this problem?

The top side AB (red line) and bottom side DC are parallel. The height of 0.5 cm is the perpendicular distance between these parallel sides.

Can I solve this by rearranging the formula first?

Yes! You can rearrange to get: $AB = \frac{2 \times Area}{h} - DC$ . This gives you $AB = \frac{2 \times 1.375}{0.5} - 4 = 5.5 - 4 = 1.5$ cm.

What if I mixed up which measurement is the height?

The height is always the perpendicular distance between the parallel sides, not the slanted sides. In this diagram, the 0.5 cm is clearly marked as the vertical distance.

How do I check my answer makes sense?

The red side AB = 1.5 cm should be shorter than the bottom side DC = 4 cm for this trapezoid shape. Also, substitute back: $\frac{(1.5+4)}{2} \times 0.5 = 1.375$ ✓

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Trapezoid Area 1.375 cm²: Find the Red Side Length

Trapezoid Area Formula with Unknown Side

❤️ 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

Why is the trapezoid formula different from rectangle?

Which sides are the parallel ones in this problem?

Can I solve this by rearranging the formula first?

What if I mixed up which measurement is the height?

How do I check my answer makes sense?

🌟 Unlock Your Math Potential

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