Calculate Parallelogram Area: Given Perimeter 47cm and Height 6

Q: Why can't I use side BC (length 6) as the height?

Because BC is a slanted side, not the perpendicular height! The height must be the perpendicular distance between the parallel sides AB and CD, which is 8 cm in this diagram.

Q: How do I know which sides are equal in a parallelogram?

In any parallelogram, opposite sides are always equal. So AB = CD and BC = AD. Use this property to set up your perimeter equation correctly.

Q: What if I get confused about which measurement to use for area?

Remember: Area = base × height. The base can be any side, but the height must be perpendicular to that base. Look for the dashed line showing the perpendicular distance!

Q: Can I use a different side as the base?

Absolutely! You could use BC = 6 as the base, but then you'd need the height perpendicular to BC. Either way gives the same area: $ 17.5 \times 8 = 140 $ cm².

Q: How do I solve for the unknown side from the perimeter?

Set up the equation: $ 2 \times AB + 2 \times BC = 47 $. Since BC = 6, you get $ 2 \times AB + 12 = 47 $, so $ AB = 17.5 $ cm.

Parallelogram Area with Given Perimeter

ABCD is a parallelogram.

Its perimeter is 47 cm.

What is its area?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the area of the parallelogram

00:03 Opposite sides are equal in a parallelogram

00:14 The perimeter of the parallelogram equals the sum of its sides

00:25 Substitute appropriate values and solve for AB

00:45 Isolate AB

00:59 This is the length of AB

01:06 Opposite sides are equal in a parallelogram

01:13 Calculate the parallelogram's area using height(H) multiplied by side(DC)

01:24 Substitute appropriate values and solve for the area

01:30 And this is the solution to the problem

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

ABCD is a parallelogram.

Its perimeter is 47 cm.

What is its area?

Step-by-step solution

First, let's remember that the perimeter of a parallelogram is the sum of its sides,

which is

AB+BC+CD+DA

We recall that in a parallelogram, opposite sides are equal, so
BC=AD=6

Let's substitute in the formula:

2AB+12=47

2AB=35

AB=17.5

Now, after finding the missing sides, we can continue to calculate the area.

Remember, the area of a parallelogram is side*height to the side.

17.5*8= 140

Final Answer

$140$ cm²

Key Points to Remember

Essential concepts to master this topic

Perimeter Formula: In parallelograms, opposite sides are equal: $P = 2a + 2b$
Side Calculation: From perimeter 47 and one side 6: $2 \times 17.5 + 2 \times 6 = 47$
Area Check: Base × height gives $17.5 \times 8 = 140$ cm² ✓

Common Mistakes

Avoid these frequent errors

Using the wrong height measurement
Don't use the slanted side length as height = wrong area calculation! The height must be perpendicular to the base, not the diagonal measurement. Always use the perpendicular distance between parallel sides as your height.

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

Why can't I use side BC (length 6) as the height?

Because BC is a slanted side, not the perpendicular height! The height must be the perpendicular distance between the parallel sides AB and CD, which is 8 cm in this diagram.

How do I know which sides are equal in a parallelogram?

In any parallelogram, opposite sides are always equal. So AB = CD and BC = AD. Use this property to set up your perimeter equation correctly.

What if I get confused about which measurement to use for area?

Remember: Area = base × height. The base can be any side, but the height must be perpendicular to that base. Look for the dashed line showing the perpendicular distance!

Can I use a different side as the base?

Absolutely! You could use BC = 6 as the base, but then you'd need the height perpendicular to BC. Either way gives the same area: $17.5 \times 8 = 140$ cm².

How do I solve for the unknown side from the perimeter?

Set up the equation: $2 \times AB + 2 \times BC = 47$ . Since BC = 6, you get $2 \times AB + 12 = 47$ , so $AB = 17.5$ cm.

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Calculate Parallelogram Area: Given Perimeter 47cm and Height 6

Parallelogram Area with Given Perimeter

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can't I use side BC (length 6) as the height?

How do I know which sides are equal in a parallelogram?

What if I get confused about which measurement to use for area?

Can I use a different side as the base?

How do I solve for the unknown side from the perimeter?

🌟 Unlock Your Math Potential

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