Calculate X in Trapezoid: Area 45 with Height 5

Q: How do I tell which sides are the bases in a trapezoid?

The bases are the two parallel sides of the trapezoid. In this figure, the top and bottom horizontal lines are parallel, so they are the bases. The height is always perpendicular to these parallel sides.

Q: Why isn't this just base times height like a rectangle?

A trapezoid has two different base lengths, unlike a rectangle where opposite sides are equal. The formula $ \frac{(b_1 + b_2) \times h}{2} $ averages the two bases first, then multiplies by height.

Q: What if I get confused about which measurement is which?

Look for right angle markers (small squares) in the diagram! The height is always the line segment that forms right angles with both parallel bases.

Trapezoid Area Formula with Unknown Dimension

Calculate X based on the data from the figure:

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find X

00:03 Opposite sides are equal in a parallelogram

00:06 Use the formula for calculating parallelogram area (base times height)

00:09 Substitute appropriate values and solve for X

00:12 Isolate X

00:15 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 based on the data from the figure:

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given information.
Step 2: Apply the appropriate formula for a parallelogram's area.
Step 3: Rearrange and calculate the unknown $X$ .

Now, let's work through each step:

Step 1: We have that the area $S$ is $45$ and the base $b$ is $5$ .

Step 2: We use the formula for the area of a parallelogram $S = b \times h$ , where in this case, $h$ is $X$ . So, we have:

$45 = 5 \times X$

Step 3: Rearrange the equation to solve for $X$ :

$X = \frac{45}{5}$

$X = 9$

Therefore, the length of side $X$ is $9$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area of trapezoid = $\frac{(b_1 + b_2) \times h}{2}$
Technique: With bases 5 and X, height 5: $45 = \frac{(5 + X) \times 5}{2}$
Check: Substitute X = 9: $\frac{(5 + 9) \times 5}{2} = 35 \neq 45$ ✓

Common Mistakes

Avoid these frequent errors

Misidentifying the trapezoid dimensions
Don't assume the figure shows what each number represents without careful analysis = wrong formula application! Students often confuse which measurements are bases versus height. Always identify the parallel sides (bases) and perpendicular distance (height) before applying the trapezoid area formula.

Practice Quiz

Test your knowledge with interactive questions

A parallelogram has a length equal to 6 cm and a height equal to 4.5 cm.

Calculate the area of the parallelogram.

FAQ

Everything you need to know about this question

How do I tell which sides are the bases in a trapezoid?

The bases are the two parallel sides of the trapezoid. In this figure, the top and bottom horizontal lines are parallel, so they are the bases. The height is always perpendicular to these parallel sides.

Why isn't this just base times height like a rectangle?

A trapezoid has two different base lengths, unlike a rectangle where opposite sides are equal. The formula $\frac{(b_1 + b_2) \times h}{2}$ averages the two bases first, then multiplies by height.

What if I get confused about which measurement is which?

Look for right angle markers (small squares) in the diagram! The height is always the line segment that forms right angles with both parallel bases.

Can I solve this problem differently?

Yes! You could also think of it as finding the average of the two bases: $\frac{5 + X}{2}$ , then multiplying by height 5 to get area 45.

How do I check if my answer makes sense?

Substitute your value back into the area formula and see if you get 45. Also, check that your answer is reasonable - if one base is 5, the other base should be a similar size for this area.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parallelogram 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