Calculate Parallelogram Area: Square with 15cm Sides and 60% Reduction

Q: What does '60% smaller' actually mean?

When something is 60% smaller, you subtract 60% from the original. So AK = 15 - (0.60 × 15) = 15 - 9 = 6 cm.

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

In a parallelogram, the height is always the perpendicular distance between parallel sides. The base can be any side, and height is measured at a right angle to it.

Q: Why isn't the area 15 × 15 = 225 cm²?

That would be the area of the square ABCD. But we need the area of parallelogram ABEF, which has base AB = 15 cm and height AK = 6 cm.

Parallelogram Area with Percentage Calculations

ABCD is a square whose length of its sides is 15 cm

ABEF is a parallelogram

AK is smaller by 60% of the side of the square
What is the area of the parallelogram ABFE?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the area of parallelogram ABEF

00:03 Side AK is the height of the parallelogram

00:11 The ratio of sides according to the given data

00:18 Substitute appropriate value for the side to find the height

00:28 To find the area of the parallelogram, multiply the height(AK) by side (AB)

00:39 Substitute appropriate values and solve to find the area

00:43 And this is the solution to the question

Step-by-step written solution

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Understand the problem

ABCD is a square whose length of its sides is 15 cm

ABEF is a parallelogram

AK is smaller by 60% of the side of the square
What is the area of the parallelogram ABFE?

Final Answer

90 cm²

Key Points to Remember

Essential concepts to master this topic

Formula: Parallelogram area equals base times height (perpendicular distance)
Percentage: 60% smaller means AK = 15 - (0.60 × 15) = 6 cm
Check: Base × height = 15 × 6 = 90 cm² ✓

Common Mistakes

Avoid these frequent errors

Using the reduced length as the height incorrectly
Don't assume AK = 40% of 15 cm = 6 cm is automatically the height! This leads to wrong area calculations. Always identify which measurement represents the perpendicular height of the parallelogram.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

What does '60% smaller' actually mean?

When something is 60% smaller, you subtract 60% from the original. So AK = 15 - (0.60 × 15) = 15 - 9 = 6 cm.

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

In a parallelogram, the height is always the perpendicular distance between parallel sides. The base can be any side, and height is measured at a right angle to it.

Why isn't the area 15 × 15 = 225 cm²?

That would be the area of the square ABCD. But we need the area of parallelogram ABEF, which has base AB = 15 cm and height AK = 6 cm.

Can I use a different side as the base?

Yes! You could use AF as the base, but then you'd need to find the perpendicular height from AF to BE. Using AB as base with height AK = 6 cm is simpler.

How do I verify my answer is correct?

Check that your dimensions make sense: base = 15 cm, height = 6 cm, so area = $15 \times 6 = 90 \text{ cm}^2$ . Also verify that 6 cm is indeed 60% less than 15 cm ✓

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