Solve for X: Trapezoid with Area 60 and Bases 8 and 14

Q: How do I identify which measurements are the parallel bases?

Look for the two horizontal lines in the trapezoid diagram. In this problem, the parallel bases are labeled 8 (top) and 14 (bottom). The height is the perpendicular distance between them, which is 5.

Q: What does X represent in this trapezoid problem?

Looking at the diagram, X appears to be a segment length on the bottom base. However, the given information shows the full bottom base is 14, and we need to use the complete trapezoid area formula with the given measurements.

Q: Why can't I just divide the area by the height to find X?

That would work for rectangles, but trapezoids have two different base lengths! You need to use the complete formula: $ Area = \frac{1}{2}(b_1 + b_2) \times h $ and solve algebraically.

Q: How do I solve for X when I have the area formula?

Step 1: Write the equation: $ 60 = \frac{1}{2}(8 + 14) \times 5 $Step 2: Simplify: $ 60 = \frac{1}{2} \times 22 \times 5 = 55 $Wait - this doesn't work! Re-examine what X represents in the specific diagram.

Q: What if my calculated area doesn't match the given area?

This means you need to reconsider what X represents. Look carefully at the diagram - X might be the height, part of a base, or another measurement that affects the area calculation. Always double-check your interpretation of the diagram!

Trapezoid Area with Unknown Base

Calculate X according to the data in the figure:

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Use the formula for calculating trapezoid area

00:07 ((sum of bases) times height) divided by 2

00:11 Substitute appropriate values according to the given data and solve for X

00:19 Divide 5 by 2

00:28 Substitute the area value and solve for X

00:34 Isolate X

00:37 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Calculate X according to the data in the figure:

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area = $\frac{1}{2}(b_1 + b_2) \times h$ for trapezoid calculations
Technique: Substitute known values: $60 = \frac{1}{2}(8 + 14) \times 5$
Check: Calculate area with X = 2: $\frac{1}{2}(8 + 14) \times 5 = 55 \neq 60$ ✓

Common Mistakes

Avoid these frequent errors

Using wrong trapezoid formula or confusing base measurements
Don't use triangle area formula (½ × base × height) for trapezoids = missing half the shape! Trapezoids need BOTH parallel bases in the formula. Always use Area = ½(base₁ + base₂) × height with the correct base measurements.

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 identify which measurements are the parallel bases?

Look for the two horizontal lines in the trapezoid diagram. In this problem, the parallel bases are labeled 8 (top) and 14 (bottom). The height is the perpendicular distance between them, which is 5.

What does X represent in this trapezoid problem?

Looking at the diagram, X appears to be a segment length on the bottom base. However, the given information shows the full bottom base is 14, and we need to use the complete trapezoid area formula with the given measurements.

Why can't I just divide the area by the height to find X?

That would work for rectangles, but trapezoids have two different base lengths! You need to use the complete formula: $Area = \frac{1}{2}(b_1 + b_2) \times h$ and solve algebraically.

How do I solve for X when I have the area formula?

Step 1: Write the equation: $60 = \frac{1}{2}(8 + 14) \times 5$

Step 2: Simplify: $60 = \frac{1}{2} \times 22 \times 5 = 55$

Wait - this doesn't work! Re-examine what X represents in the specific diagram.

What if my calculated area doesn't match the given area?

This means you need to reconsider what X represents. Look carefully at the diagram - X might be the height, part of a base, or another measurement that affects the area calculation. Always double-check your interpretation of the diagram!

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