Trapezoid Area Problem: Finding AB When Area = 77 and Height = 7

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

In a trapezoid, the parallel sides are the bases. From the diagram, AB and CD are horizontal and parallel, so they're the bases. The height is the perpendicular distance between these parallel sides.

Q: Why do we add the two bases together in the formula?

Think of a trapezoid as the average of two rectangles! Adding the bases and dividing by 2 gives you the average base length, then multiply by height for the area.

Q: What if I get a decimal answer instead of a whole number?

That's completely normal! Many geometry problems have decimal or fractional answers. Just make sure your calculations are correct and round appropriately if needed.

Q: Can I solve this problem differently?

Yes! You could also think of it as solving the equation $ 154 = 7(AB + 12) $ after multiplying both sides by 2. The algebraic approach is the same - just different steps!

Q: How do I remember the trapezoid area formula?

Remember: "Half times sum times height". It's like finding the area of a rectangle with the average of the two base lengths: $ A = \frac{1}{2}(b_1 + b_2) \times h $

Trapezoid Area Formula with Given Measurements

Given the trapeze in front of you:

Given h=7, CD=12.

Since the area of the trapezoid ABCD is equal to 77.

Find the length of the side AB.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find AB

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

00:13 We'll substitute appropriate values and solve for AB

00:24 Divide by 7

00:33 Multiply by 2 to eliminate the fraction

00:41 Isolate AB

00:52 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 trapeze in front of you:

Given h=7, CD=12.

Since the area of the trapezoid ABCD is equal to 77.

Find the length of the side AB.

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: Solve for the unknown side $AB$

Now, let's work through each step:
Step 1: The problem gives us the height $h = 7$ , the base $CD = 12$ , and the area $A = 77$ . We need to find the length of $AB$ .
Step 2: We'll use the formula for the area of a trapezoid: $A = \frac{1}{2} (b_1 + b_2) \times h$ which gives us: $77 = \frac{1}{2} (AB + 12) \times 7$
Step 3: Simplifying the equation: $77 = \frac{7}{2} (AB + 12)$ Multiply both sides by 2 to clear the fraction: $154 = 7 (AB + 12)$ Divide both sides by 7: $22 = AB + 12$ Subtract 12 from both sides to solve for $AB$ : $AB = 10$

Therefore, the solution to the problem is $AB = 10$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Trapezoid area equals half times sum of bases times height
Technique: Substitute known values: $77 = \frac{1}{2}(AB + 12) \times 7$
Check: Verify by substituting AB = 10 back into area formula ✓

Common Mistakes

Avoid these frequent errors

Using wrong trapezoid area formula
Don't use triangle area formula $A = \frac{1}{2} \times base \times height$ = wrong answer! Trapezoids have two parallel bases, not one. Always use $A = \frac{1}{2}(b_1 + b_2) \times h$ for trapezoids.

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 parallel bases?

In a trapezoid, the parallel sides are the bases. From the diagram, AB and CD are horizontal and parallel, so they're the bases. The height is the perpendicular distance between these parallel sides.

Why do we add the two bases together in the formula?

Think of a trapezoid as the average of two rectangles! Adding the bases and dividing by 2 gives you the average base length, then multiply by height for the area.

What if I get a decimal answer instead of a whole number?

That's completely normal! Many geometry problems have decimal or fractional answers. Just make sure your calculations are correct and round appropriately if needed.

Can I solve this problem differently?

Yes! You could also think of it as solving the equation $154 = 7(AB + 12)$ after multiplying both sides by 2. The algebraic approach is the same - just different steps!

How do I remember the trapezoid area formula?

Remember: "Half times sum times height". It's like finding the area of a rectangle with the average of the two base lengths: $A = \frac{1}{2}(b_1 + b_2) \times h$

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