Solve for X: Parallelogram Area 392 cm² with 2X and 4X Expressions

Parallelogram Area with Algebraic Expressions

The area of the parallelogram ABCD is 392 cm².

Calculate X.

2X2X2X4X4X4XAAABBBCCCDDDEEE

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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
00:06 Side(BC) times height (AE)
00:13 Substitute appropriate values and solve for X
00:30 Isolate X
00:36 Extract the root to find X
00:45 The two options for X
00:48 X must be positive as it represents a side length

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The area of the parallelogram ABCD is 392 cm².

Calculate X.

2X2X2X4X4X4XAAABBBCCCDDDEEE

2

Step-by-step solution

To find X X , we use the formula for the area of a parallelogram:

Area=base×height \text{Area} = \text{base} \times \text{height}

Given that the area is 392 cm2^2, and assuming 2X 2X is the base and 4X 4X is the height, we substitute these values into the formula:

392=(2X)×(4X) 392 = (2X) \times (4X)

Simplifying the right side gives us:

392=2⋅4⋅X2=8X2 392 = 2 \cdot 4 \cdot X^2 = 8X^2

To solve for X2 X^2 , divide both sides by 8:

X2=3928 X^2 = \frac{392}{8}

X2=49 X^2 = 49

Taking the square root of both sides, we find:

X=49 X = \sqrt{49}

X=7 X = 7

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

3

Final Answer

7 7 cm

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of parallelogram equals base times height
  • Technique: Set up equation (2X)×(4X)=8X2=392 (2X) \times (4X) = 8X^2 = 392
  • Check: Verify 2(7)×4(7)=14×28=392 2(7) \times 4(7) = 14 \times 28 = 392 ✓

Common Mistakes

Avoid these frequent errors
  • Adding expressions instead of multiplying
    Don't calculate 2X+4X=6X 2X + 4X = 6X for area formula = completely wrong answer! Area requires multiplication of base and height, not addition. Always multiply the two dimensions: (2X)×(4X)=8X2 (2X) \times (4X) = 8X^2 .

Practice Quiz

Test your knowledge with interactive questions

Calculate the area of the parallelogram according to the data in the diagram.

101010777AAABBBCCCDDDEEE

FAQ

Everything you need to know about this question

How do I know which sides represent base and height?

+

In parallelograms, any adjacent sides can be treated as base and height. The diagram shows 2X 2X and 4X 4X as adjacent sides, so we multiply them together.

Why do we get 8X2 8X^2 when multiplying?

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When you multiply 2X×4X 2X \times 4X , you multiply the numbers: 2×4=8 2 \times 4 = 8 , and multiply the variables: X×X=X2 X \times X = X^2 . Combined: 8X2 8X^2 .

What if I get a negative value when taking the square root?

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Since length measurements must be positive, we only consider the positive square root. X=7 X = 7 cm, not -7 cm.

Can I use different sides as base and height?

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The area formula works with any two adjacent sides of a parallelogram. In this problem, we're given expressions for two adjacent sides, so we multiply them directly.

How do I check if 7 cm is really correct?

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Substitute back: Base = 2(7)=14 2(7) = 14 cm, Height = 4(7)=28 4(7) = 28 cm. Area = 14×28=392 14 \times 28 = 392 cm² ✓

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