Calculate Parallelogram Area: Using Base 8 and Height 4

Area Formulas with Perpendicular Height

Given the parallelogram of the figure

What is your area?

888444AAABBBCCCDDDEEE

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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
00:21 Calculate the area of the parallelogram using height(AE) multiplied by side(DC)
00:31 Substitute appropriate values and solve to find the area
00:36 And this is the solution to the problem

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?

888444AAABBBCCCDDDEEE

2

Step-by-step solution

To solve the problem of finding the area of the parallelogram, we follow these steps:

  • Step 1: Identify the relevant dimensions from the figure.
  • Step 2: Apply the formula for the area of a parallelogram.
  • Step 3: Perform the multiplication to calculate the area.

Let's work through each step:

Step 1: From the problem description and figure, we have:

  • The base AB=8 AB = 8 cm.
  • The height DE=4 DE = 4 cm, which is perpendicular to the base AB AB .

Step 2: Use the formula for the area of a parallelogram:

Area=base×height \text{Area} = \text{base} \times \text{height}

Substituting the given values into the formula:

Area=8cm×4cm \text{Area} = 8 \, \text{cm} \times 4 \, \text{cm}

Step 3: Calculate:

Area=32cm2 \text{Area} = 32 \, \text{cm}^2

Therefore, the area of the parallelogram is 32cm2\mathbf{32 \, \text{cm}^2}.

3

Final Answer

32 32 cm².

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area of parallelogram equals base times perpendicular height
  • Technique: Identify base = 8 and height = 4, then multiply: 8 × 4 = 32
  • Check: Verify height is perpendicular to base, not slanted side ✓

Common Mistakes

Avoid these frequent errors
  • Using slanted side instead of perpendicular height
    Don't multiply base by the slanted side length = wrong area! The slanted side is longer than the actual height. Always use the perpendicular distance from base to 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 use the slanted side for height?

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The slanted side is longer than the actual height! Area needs the perpendicular distance between parallel sides, not the diagonal measurement along the slant.

How do I identify the height in the diagram?

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Look for the perpendicular line (shown as a dashed vertical line with a right angle symbol). The height is always at a 90° angle to the base, not slanted.

What if I get different numbers for base and height?

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It doesn't matter which parallel side you choose as the base! Just make sure you use the corresponding perpendicular height for whichever base you pick.

Is this the same formula for rectangles?

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Yes! Rectangles are special parallelograms where all angles are 90°. The formula Area=base×height \text{Area} = \text{base} \times \text{height} works for both.

Why is my answer in square units?

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Area measures 2-dimensional space, so we always use square units like cm², m², or ft². You're measuring how many unit squares fit inside the shape!

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