Parallelogram Area Comparison: Two Shapes with Height 4cm and Base 6cm

Q: Why don't the different shapes affect the area?

Both parallelograms use the same base BC = 6 cm and the same perpendicular height = 4 cm. Since area = base × height, they must have equal areas regardless of their different orientations!

Q: What if I measured the slanted sides instead?

The slanted sides like AD and CF are not the height! Height must be the perpendicular distance between parallel sides. Only BG = 4 cm is the correct height measurement.

Q: How can I tell which measurement is the height?

Look for the perpendicular line with a right angle symbol (small square). In this problem, BG is drawn vertically with the right angle marker, showing it's the true height.

Q: Do all parallelograms with the same base and height have equal areas?

Yes, absolutely! The area formula Area = base × height means any parallelogram with base = 6 cm and height = 4 cm will have area = 24 cm², no matter how 'slanted' it looks.

Q: Why does BC = 6 work as the base for both shapes?

BC is a shared side between both parallelograms ABCD and BCEF. Since it's horizontal and measures 6 cm, it serves as the base for calculating both areas.

Parallelogram Area with Shared Dimensions

Look at the two parallelograms ABCD and BCEF below.

AB is parallel to CD

CE is parallel to BF

BG is a height equal to 4 cm

$BC=6$

Are their areas equal?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Are the areas equal?

00:03 Let's use the formula for calculating the area of a parallelogram (base times height)

00:12 Opposite sides are equal in a parallelogram

00:16 Let's substitute appropriate values according to the given data and solve to find the area

00:19 This is area ABCD, now let's find area BCEF

00:23 Let's use the formula for calculating the area of a parallelogram (base times height)

00:28 Opposite sides are equal in a parallelogram

00:33 Let's substitute appropriate values according to the given data and solve to find the area

00:37 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the two parallelograms ABCD and BCEF below.

AB is parallel to CD

CE is parallel to BF

BG is a height equal to 4 cm

$BC=6$

Are their areas equal?

Final Answer

The areas are equal.

Key Points to Remember

Essential concepts to master this topic

Formula: Area of parallelogram equals base times perpendicular height
Technique: Both shapes use BC = 6 cm as base and height = 4 cm
Check: Calculate 6 × 4 = 24 cm² for both parallelograms ✓

Common Mistakes

Avoid these frequent errors

Using slanted sides instead of perpendicular height
Don't measure the slanted sides AD or CF as the height = wrong area calculation! The slanted sides are longer than the perpendicular distance. Always use the perpendicular height BG = 4 cm, not the slanted edges.

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

Why don't the different shapes affect the area?

Both parallelograms use the same base BC = 6 cm and the same perpendicular height = 4 cm. Since area = base × height, they must have equal areas regardless of their different orientations!

What if I measured the slanted sides instead?

The slanted sides like AD and CF are not the height! Height must be the perpendicular distance between parallel sides. Only BG = 4 cm is the correct height measurement.

How can I tell which measurement is the height?

Look for the perpendicular line with a right angle symbol (small square). In this problem, BG is drawn vertically with the right angle marker, showing it's the true height.

Do all parallelograms with the same base and height have equal areas?

Yes, absolutely! The area formula Area = base × height means any parallelogram with base = 6 cm and height = 4 cm will have area = 24 cm², no matter how 'slanted' it looks.

Why does BC = 6 work as the base for both shapes?

BC is a shared side between both parallelograms ABCD and BCEF. Since it's horizontal and measures 6 cm, it serves as the base for calculating both areas.

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