Calculate Side DC in Parallelogram ABCD with Area 72Y cm²

Parallelogram Area with Variable Expressions

The area of parallelogram ABCD is 72Y cm².

Calculate DC.

999AAABBBCCCDDDEEE

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Express DC using Y
00:03 We'll use the formula for calculating the area of a parallelogram
00:06 side(DC) multiplied by height (AE)
00:20 We'll substitute appropriate values and solve for DC
00:42 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

The area of parallelogram ABCD is 72Y cm².

Calculate DC.

999AAABBBCCCDDDEEE

2

Step-by-step solution

To find the side length DC DC of parallelogram ABCD ABCD with an area of 72ycm2 72y \, \text{cm}^2 :

  • Given: Area = 72ycm2 72y \, \text{cm}^2 and height = 9cm 9 \, \text{cm} (from the base).
  • Formula for area: Area=base×height \text{Area} = \text{base} \times \text{height} .
  • Rearrange to solve for base DC DC : base=Areaheight \text{base} = \frac{\text{Area}}{\text{height}} .
  • Substitute the given values: base=72y9 \text{base} = \frac{72y}{9} .
  • Simplify: base=8y \text{base} = 8y .

Therefore, the length of DC DC is 8ycm 8y \, \text{cm} .

3

Final Answer

8y 8y

Key Points to Remember

Essential concepts to master this topic
  • Area Formula: Area = base × height for parallelograms
  • Technique: Rearrange to base = Area ÷ height = 72y ÷ 9
  • Check: Verify 8y × 9 = 72y matches given area ✓

Common Mistakes

Avoid these frequent errors
  • Confusing base and height measurements
    Don't use the slanted side as the height = wrong calculation! The height must be perpendicular to the base, not the diagonal side length. Always identify the perpendicular height (9 cm) from the diagram.

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 side is the base and which is the height?

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The base can be any side of the parallelogram, but the height must be the perpendicular distance between parallel sides. Look for the dashed line marked with 9 - that's your height!

Why is the answer 8y instead of just 8?

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The area is given as 72y 72y , which contains the variable y. When you divide 72y÷9=8y 72y \div 9 = 8y , the variable stays in your answer.

Can I use a different side as the base?

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Yes! You could use side AD as the base, but then you'd need the perpendicular height to that side. The calculation Area = base × height always works regardless of which side you choose as base.

What does the variable y represent in this problem?

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The variable y represents an unknown value with units of length (cm). It could be any positive number - the relationship between area and sides stays the same regardless of y's actual value.

How can I check if 8y is correct?

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Multiply your answer by the height: 8y×9=72y 8y \times 9 = 72y . This matches the given area, so 8y cm is correct!

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