Calculate Trapezoid Area: Finding Space Between 5 and 7 Unit Bases

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

The bases are the two parallel sides of the trapezoid. Look for sides that are horizontal or have the same angle. In this problem, AB (top) = 5 and DC (bottom) = 7 are parallel.

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

The height is always the perpendicular distance between the parallel bases. From the diagram, we can see the height is $ \frac{8}{3} $ units.

Q: Why do we divide by 2 in the formula?

Think of a trapezoid as the average of the two bases multiplied by height. $ \frac{b_1 + b_2}{2} $ gives the average base length, then multiply by height for area.

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, you need different formulas.

Trapezoid Area with Parallel Base Measurements

Given the following trapezoid:

Find 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 Let's use the formula for calculating the area of a trapezoid

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

00:14 Let's substitute appropriate values and solve to find the area

00:26 Combine numerator with numerator and denominator with denominator

00:31 Divide 12 by 6

00:36 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:

Find the area of the trapezoid ABCD.

Step-by-step solution

The area of the trapezoid will be:

$S=\frac{(AB+DC)\times h}{2}$

We replace the known data in the formula:

$\frac{(5+7)}{2}\times\frac{8}{3}=$

$\frac{12\times8}{6}=$

$\frac{96}{6}=16$

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area equals sum of parallel bases times height divided by two
Technique: $A = \frac{(b_1 + b_2) \times h}{2} = \frac{(5+7) \times \frac{8}{3}}{2}$
Check: Verify bases are parallel and height is perpendicular: 12 × 8/3 ÷ 2 = 16 ✓

Common Mistakes

Avoid these frequent errors

Using the wrong sides as bases
Don't use the slanted sides AD and BC as bases = wrong formula application! Only parallel sides count as bases in the trapezoid area formula. Always identify which sides are parallel (AB = 5 and DC = 7) before calculating.

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. Look for sides that are horizontal or have the same angle. In this problem, AB (top) = 5 and DC (bottom) = 7 are parallel.

What if the height isn't given directly?

The height is always the perpendicular distance between the parallel bases. From the diagram, we can see the height is $\frac{8}{3}$ units.

Why do we divide by 2 in the formula?

Think of a trapezoid as the average of the two bases multiplied by height. $\frac{b_1 + b_2}{2}$ gives the average base length, then multiply by height for area.

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, you need different formulas.

What if I get a fraction in my calculation?

Fractions are normal in geometry! Just be careful with your arithmetic: $\frac{12 \times 8}{3 \times 2} = \frac{96}{6} = 16$

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