Calculate Parallelogram Area: Using Base 9 and Height 5

Parallelogram Area with Perpendicular Height

Given the parallelogram of the figure

What is your area?

999555AAABBBCCCDDDEEE

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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 Calculate the area of the parallelogram using height(DE) multiplied by side(BC)
00:11 Substitute appropriate values and solve to find the area
00:23 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Given the parallelogram of the figure

What is your area?

999555AAABBBCCCDDDEEE

2

Step-by-step solution

The area of a parallelogram is calculated using the formula A=base×height A = \text{base} \times \text{height} .

From the figure, we identify the base BC BC as 9 cm and the perpendicular distance (height) from point E E to BC BC as 5 cm.

Substituting into the formula for area, we have:

A=9cm×5cm=45cm2 A = 9 \, \text{cm} \times 5 \, \text{cm} = 45 \, \text{cm}^2

Therefore, the area of the parallelogram is 45cm2 45 \, \text{cm}^2 .

Looking at the provided answer choices, the correct choice is:

45 45 cm².

3

Final Answer

45 45 cm².

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of parallelogram equals base times perpendicular height
  • Technique: Identify base = 9 cm and height = 5 cm from diagram
  • Check: Verify units match and height is perpendicular to base ✓

Common Mistakes

Avoid these frequent errors
  • Using slanted side length instead of perpendicular height
    Don't use the slanted side BC as height = wrong area calculation! The slanted side is longer than the perpendicular distance and gives an overestimate. Always use the perpendicular distance from the base to the opposite side.

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

Why can't I just multiply any two sides of the parallelogram?

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Because parallelograms are slanted! You need the perpendicular height, not the slanted side length. Think of it like measuring the actual vertical distance between two parallel lines.

How do I identify the height in the diagram?

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Look for the perpendicular line from one side to the opposite parallel side. In this problem, it's the line from point E to side BC, marked as 5 cm with a right angle symbol.

What if the base and height aren't clearly labeled?

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You can use any side as the base, but then you must find the perpendicular distance to the opposite parallel side. The formula A=base×height A = base \times height always works!

Is this the same as rectangle area?

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Yes, the formula is the same! But rectangles have all right angles, so any adjacent side can be the height. Parallelograms are slanted, so you must use perpendicular height.

Can the area formula work with different units?

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Absolutely! Just make sure both measurements use the same units. If base is in meters and height in centimeters, convert one to match the other first.

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