Area Calculation: Finding Parallelogram Area Using Rectangle Area of 35 cm²

Q: Why isn't the parallelogram area the same as the rectangle area?

The parallelogram ABCD extends beyond the rectangle AEFD by the length CF = 2 cm. So while they share the same height, the parallelogram has a longer base (9 cm vs 7 cm).

Q: How do I find the height of the parallelogram?

The height is the same as the rectangle's width! Since Area = length × width for the rectangle, we get $ ED = \frac{35}{7} = 5 $ cm.

Q: What if the diagram looks confusing with all the shapes?

Focus on what you know: The rectangle AEFD gives you the height (ED = 5), and you can find the full base by adding AF + FC = 7 + 2 = 9 cm.

Q: Can I use a different formula for parallelogram area?

Yes! You can use $ Area = base \times height $ where the height is perpendicular to the base. Here, ED = 5 is perpendicular to the base CD = 9.

Q: How do I know which measurements to use?

For parallelogram area, you need a base and its corresponding height. The rectangle shows that ED = 5 is the height, and CD = AF + FC = 9 is the base.

Parallelogram Areas with Rectangle Relationships

ABCD is a parallelogram and AEFD is a rectangle.

AE = 7

The area of AEFD is 35 cm².

CF = 2

What is the area of the parallelogram?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Determine the area of the parallelogram ABDC

00:04 Apply the formula for the area of a rectangle: side(AE) multiplied by side(ED)

00:11 Insert the relevant values into the forma and proceed to solve for ED

00:14 Isolate ED

00:19 This is the length of side ED

00:26 Opposite sides are equal in a rectangle

00:30 The whole side equals the sum of its parts

00:41 Apply the formula for the area of a parallelogram

00:44 height(ED) multiplied by base(CD)

00:47 Insert the relevant values into the formula and proceed to solve for the area

00:50 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

ABCD is a parallelogram and AEFD is a rectangle.

AE = 7

The area of AEFD is 35 cm².

CF = 2

What is the area of the parallelogram?

Step-by-step solution

Let's first calculate the sides of the rectangle:

$AEDF=AE\times ED$

Let's input the known data:

$35=7\times ED$

Let's divide the two legs by 7:

$ED=5$

Since AEDF is a rectangle, we can claim that:

ED=FD=7

Let's calculate side CD:

$2+7=9$

Let's calculate the area of parallelogram ABCD:

$ABCD=CD\times ED$

Let's input the known data:

$ABCD=9\times5=45$

Final Answer

45 cm².

Key Points to Remember

Essential concepts to master this topic

Rectangle Formula: Area equals length times width to find missing dimensions
Technique: Use $35 = 7 \times ED$ to find ED = 5 cm
Check: Parallelogram area = 9 × 5 = 45 cm² matches rectangle base ✓

Common Mistakes

Avoid these frequent errors

Using rectangle area as parallelogram area
Don't assume the parallelogram ABCD has the same area as rectangle AEFD = 35 cm²! The parallelogram extends beyond the rectangle by CF = 2 cm, making it larger. Always calculate the full base length: AF + FC = 7 + 2 = 9 cm.

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 isn't the parallelogram area the same as the rectangle area?

The parallelogram ABCD extends beyond the rectangle AEFD by the length CF = 2 cm. So while they share the same height, the parallelogram has a longer base (9 cm vs 7 cm).

How do I find the height of the parallelogram?

The height is the same as the rectangle's width! Since Area = length × width for the rectangle, we get $ED = \frac{35}{7} = 5$ cm.

What if the diagram looks confusing with all the shapes?

Focus on what you know: The rectangle AEFD gives you the height (ED = 5), and you can find the full base by adding AF + FC = 7 + 2 = 9 cm.

Can I use a different formula for parallelogram area?

Yes! You can use $Area = base \times height$ where the height is perpendicular to the base. Here, ED = 5 is perpendicular to the base CD = 9.

How do I know which measurements to use?

For parallelogram area, you need a base and its corresponding height. The rectangle shows that ED = 5 is the height, and CD = AF + FC = 9 is the base.

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Area Calculation: Finding Parallelogram Area Using Rectangle Area of 35 cm²

Parallelogram Areas with Rectangle Relationships

❤️ 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 isn't the parallelogram area the same as the rectangle area?

How do I find the height of the parallelogram?

What if the diagram looks confusing with all the shapes?

Can I use a different formula for parallelogram area?

How do I know which measurements to use?

🌟 Unlock Your Math Potential

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