The area of the trapezoid in the diagram is 78 cm².Calculate X.X+10X+10X+1012X-1012X-1012X-10666

The quadratic equation is required.

It is not possible to calculate.

Solve for X: Trapezoid Area of 78 cm² with Sides (X+10) and (12X-10)

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

The trapezoid area formula uses the average of the two parallel sides (bases). Adding them together, then multiplying by ½, gives you that average length times the height.

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

The bases are the parallel sides - in this diagram, they're the top side (X+10) and bottom side (12X-10). The height (6) is always perpendicular to these parallel sides.

Q: Can I use the rectangle area formula instead?

No! A trapezoid has two different parallel sides, unlike a rectangle where opposite sides are equal. Always use $ A = \frac{1}{2}(b_1 + b_2)h $ for trapezoids.

Q: How do I handle the fractions when solving?

Multiply both sides by 2 early to eliminate the fraction: $ 78 \times 2 = 156 $. This makes the algebra simpler and reduces calculation errors.

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

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 according to the given data and solve for X

00:31 We'll group the numbers as one factor and X as another factor

00:42 We'll divide 6 by 2

00:53 We'll isolate X

01:04 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

The area of the trapezoid in the diagram is 78 cm².

Calculate X.

2

Step-by-step solution

To solve this problem, we need to apply the area formula for a trapezoid:

The area $A$ of a trapezoid is given by $A = \frac{1}{2} \times (b_1 + b_2) \times h$ where $b_1$ and $b_2$ are the base lengths, and $h$ is the height.

The problem provides:

Area $A = 78$ cm²
Base 1, $b_1 = X + 10$
Base 2, $b_2 = 12X - 10$
Height $h = 6$ cm

Substitute these into the area formula:

$78 = \frac{1}{2} \times ((X + 10) + (12X - 10)) \times 6$

Simplify the expression:

$78 = \frac{1}{2} \times (13X) \times 6$

Multiply through by 2 to clear the fraction:

$156 = 13X \times 6$

Simplify further:

$156 = 78X$

Solving for $X$ gives:

$X = \frac{156}{78}$

$X = 2$

Therefore, the solution to the problem is $X = 2$ .

3

Final Answer

$2$

Key Points to Remember

Essential concepts to master this topic

Formula: Area = $\frac{1}{2} \times (b_1 + b_2) \times h$ for trapezoids
Technique: Combine like terms: (X+10) + (12X-10) = 13X
Check: Substitute X=2: bases become 12 and 14, area = ½(26)(6) = 78 ✓

Common Mistakes

Avoid these frequent errors

Forgetting to combine like terms in the bases
Don't leave the bases as separate expressions (X+10) and (12X-10) when substituting = messy calculations! This makes the algebra much harder and leads to errors. Always combine like terms first: (X+10) + (12X-10) = 13X.

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 do I add the two bases together in the formula?

+

The trapezoid area formula uses the average of the two parallel sides (bases). Adding them together, then multiplying by ½, gives you that average length times the height.

How do I know which sides are the bases?

+

The bases are the parallel sides - in this diagram, they're the top side (X+10) and bottom side (12X-10). The height (6) is always perpendicular to these parallel sides.

What if I get a negative value for X?

+

Check if negative X makes sense! If X = -3, then X+10 = 7, but 12X-10 = -46. Since side lengths can't be negative, X must be positive in geometry problems.

Can I use the rectangle area formula instead?

+

No! A trapezoid has two different parallel sides, unlike a rectangle where opposite sides are equal. Always use $A = \frac{1}{2}(b_1 + b_2)h$ for trapezoids.

How do I handle the fractions when solving?

+

Multiply both sides by 2 early to eliminate the fraction: $78 \times 2 = 156$ . This makes the algebra simpler and reduces calculation errors.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Trapeze questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Solve for X: Trapezoid Area of 78 cm² with Sides (X+10) and (12X-10)

Trapezoid Area with Algebraic Side Lengths

❤️ 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 do I add the two bases together in the formula?

How do I know which sides are the bases?

What if I get a negative value for X?

Can I use the rectangle area formula instead?

How do I handle the fractions when solving?

🌟 Unlock Your Math Potential

More Questions

Trapeze

Trapezoid Area Problem: Express Area with Height 2X and Parallel Sides (X+14) and (3X+7)

Calculate Trapezoid Area with Equilateral Triangle and Parallelogram Properties

Calculate Trapezoid Height: Area 9 cm² with 3-Unit Base

Trapezoid Area 1.375 cm²: Find the Red Side Length

Area of a Trapezoid

Trapezoid Area Calculation: Using 3:2 Side-to-Height Ratio

Trapezoid Side Length: Finding DC When Area is 30 cm² and Base Ratio is 1:3

Calculate Trapezoid Area: Finding Area with Sides 2X and 3Y

Calculate Height AE in Trapezoid with Area 9x Square Centimeters