Calculate Parallelogram Area: Given Height h=6 and Base=13

Parallelogram Area with Given Height

Look at the parallelogram in the figure.

h = 6

What is the area of the parallelogram?

131313hhhAAABBBCCCDDD

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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
00:04 Calculate the area of the parallelogram by height(H) multiplied by side(DC)
00:10 Substitute appropriate values and solve to find the area
00:20 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Look at the parallelogram in the figure.

h = 6

What is the area of the parallelogram?

131313hhhAAABBBCCCDDD

2

Step-by-step solution

To find the area of the given parallelogram, we will use the standard formula for the area of a parallelogram, which is the product of its base and height.

  • Step 1: Identify the given dimensions.
  • Step 2: Base of the parallelogram is given as 13 13 cm.
  • Step 3: Height is given as 6 6 cm.

Now, let's proceed with the calculation:

Using the formula for the area of a parallelogram:

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

Substituting the known values:

Area=13cm×6cm \text{Area} = 13 \, \text{cm} \times 6 \, \text{cm}

Area=78cm2 \text{Area} = 78 \, \text{cm}^2

Hence, the area of the parallelogram is 78cm2\mathbf{78 \, \text{cm}^2}.

3

Final Answer

78 78 cm².

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area equals base times perpendicular height
  • Technique: Multiply base 13 by height 6 = 78
  • Check: Height must be perpendicular to base, not slanted side ✓

Common Mistakes

Avoid these frequent errors
  • Using a slanted side instead of perpendicular height
    Don't multiply base by a slanted side = wrong area! The slanted sides are longer than the perpendicular height and give inflated results. Always use the perpendicular distance between parallel bases.

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

What's the difference between height and a side of the parallelogram?

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The height is the perpendicular distance between the parallel bases. A side of the parallelogram is usually longer and at an angle. Always use height for area calculations!

Why is the formula base × height and not base × side?

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Area measures the space inside a shape. Using a slanted side would count extra space that isn't actually inside the parallelogram. The perpendicular height gives the true vertical distance.

How do I identify which measurement is the height in a diagram?

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Look for the perpendicular line - it forms a 90° angle with the base. In this problem, the vertical dashed line marked 'h' shows the true height of 6 cm.

Can I use any side as the base?

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Yes! You can choose either pair of parallel sides as your base. Just make sure to use the perpendicular height to that chosen base, not to a different side.

What if I accidentally used the wrong measurements?

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If your answer seems too big or too small, check that you used base × height, not base × side. The height should always be shorter than or equal to the slanted sides.

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