Find X in Geometric Figure: Area 21 with Side Length 3

Q: How do I know which side is the base and which is the height?

In a parallelogram, the height is always perpendicular to the base. Look for right angle marks or measurements that show the shortest distance between parallel sides. Any side can be the base - just make sure the height is perpendicular to it!

Q: Can I use any parallelogram side as the base?

Yes! You can choose any side as the base, but then you must use the perpendicular distance to the opposite side as the height, not another side length.

Q: Why can't I just multiply any two sides together?

Multiplying any two sides only works for rectangles. For parallelograms, you need one side (base) and the perpendicular distance to the opposite side (height), not just another side length.

Q: How do I check my answer is correct?

Substitute back into the area formula: $ Area = base \times height $. If $ 7 \times 3 = 21 $, and the given area is 21, then X = 7 is correct!

Parallelogram Area with Missing Side Length

Calculate X based on 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 the area of a parallelogram (base times height)

00:06 Substitute appropriate values and solve for X

00:09 Isolate X

00:12 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 in the figure:

Step-by-step solution

To solve this problem, we'll use the area formula for a parallelogram:

Step 1: Identify and assign base and height. Assume $X$ is the base and the given side (3) is the height.
Step 2: Apply the formula $S = b \times h$ , where $b$ is base and $h$ is height.
Step 3: Since $S = 21$ , substitute it into the equation $21 = X \times 3$ .
Step 4: Solve for $X$ .

Let's work through these steps:

Step 1: Assume $X$ is the base, and 3 is the height.

Step 2: Use the formula $S = b \times h = X \times 3$ .

Step 3: Substitute $S = 21$ :

21 = X \times 3

Step 4: Solve for $X$ :

X = \frac{21}{3}

Simplifying gives:

X = 7

Therefore, the solution to the problem is $X = 7$ .

Final Answer

Key Points to Remember

Essential concepts to master this topic

Formula: Area of parallelogram equals base times height
Technique: Substitute known values: 21 = X × 3, then divide
Check: Verify that 7 × 3 = 21 matches given area ✓

Common Mistakes

Avoid these frequent errors

Confusing which measurement is base versus height
Don't assume the labeled side is always the base = wrong area calculation! The height must be perpendicular to the base, not just any side length. Always identify which measurement represents the perpendicular distance between parallel sides.

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 know which side is the base and which is the height?

In a parallelogram, the height is always perpendicular to the base. Look for right angle marks or measurements that show the shortest distance between parallel sides. Any side can be the base - just make sure the height is perpendicular to it!

Can I use any parallelogram side as the base?

Yes! You can choose any side as the base, but then you must use the perpendicular distance to the opposite side as the height, not another side length.

What if the parallelogram looks like a rectangle?

A rectangle is a special type of parallelogram! The same area formula applies: $A = base \times height$ . In rectangles, adjacent sides are always perpendicular, making calculations easier.

Why can't I just multiply any two sides together?

Multiplying any two sides only works for rectangles. For parallelograms, you need one side (base) and the perpendicular distance to the opposite side (height), not just another side length.

How do I check my answer is correct?

Substitute back into the area formula: $Area = base \times height$ . If $7 \times 3 = 21$ , and the given area is 21, then X = 7 is correct!

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