Parallelogram Problem: Finding Side AD When Area = 40 cm² and Height = 4 cm

Parallelogram Area with Base Calculation

Given the parallelogram of the figure

The height of the side AD equal to 4 cm

The area of the parallelogram is equal to 40 cm².

Find AD

AAABBBCCCDDD

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:12 Let's find the length of A D.
00:15 We'll use the formula for the area of a parallelogram.
00:19 It's side A D, times the height, H.
00:24 We'll plug in the values and solve to find A D.
00:43 And that's how we solve the problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the parallelogram of the figure

The height of the side AD equal to 4 cm

The area of the parallelogram is equal to 40 cm².

Find AD

AAABBBCCCDDD

2

Step-by-step solution

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

  • The given area of the parallelogram is 40 cm².
  • The height, perpendicular to the base AD AD , is 4 cm.
  • We need to find the length of AD AD , the base of the parallelogram.

The formula for the area of a parallelogram is:

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

We can rearrange this formula to solve for the base:

base=Areaheight \text{base} = \frac{\text{Area}}{\text{height}}

Substituting the given values into the formula, we get:

base=40cm24cm \text{base} = \frac{40 \, \text{cm}^2}{4 \, \text{cm}}

Calculating this gives us:

base=10cm \text{base} = 10 \, \text{cm}

Therefore, the length of AD AD is \textbf{\( 10 } \, \text{cm} \).

3

Final Answer

10 10 cm

Key Points to Remember

Essential concepts to master this topic
  • Area Formula: Area equals base times height for parallelograms
  • Rearrangement: Base = Area ÷ Height = 40 ÷ 4 = 10 cm
  • Verification: Check that 10 × 4 = 40 cm² matches given area ✓

Common Mistakes

Avoid these frequent errors
  • Using wrong formula or measurements
    Don't use perimeter formulas or diagonal measurements = wrong calculation! The area formula specifically requires base times perpendicular height, not slanted sides. Always identify which measurement is the perpendicular height to the base.

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.

6664.54.54.5

FAQ

Everything you need to know about this question

What's the difference between height and side length in a parallelogram?

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The height is the perpendicular distance between parallel sides, while side length is the actual length of the slanted side. For area calculations, always use the perpendicular height!

Can I use any side as the base?

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Yes! You can use any side as the base, but you must use the height that's perpendicular to that specific base. Different base-height pairs will give the same area.

Why do we divide area by height to find the base?

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Because we're rearranging the formula! Since Area = Base × Height, we can solve for Base by dividing: Base=AreaHeight \text{Base} = \frac{\text{Area}}{\text{Height}}

How do I know which measurement is 4 cm in the problem?

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The problem states "the height of the side AD equal to 4 cm" - this means 4 cm is the perpendicular distance from AD to the opposite side, not the length of AD itself.

What if I get a decimal answer instead of 10?

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Check your division! 40÷4=10 40 ÷ 4 = 10 exactly. If you get decimals, double-check that you're using the correct values from the problem and dividing area by height.

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