Calculate Parallelogram Area: Using Height 7 and Base 10

Parallelogram Area with Given Base and Height

Calculate the area of the parallelogram according to the data in the diagram.

101010777AAABBBCCCDDDEEE

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1

Understand the problem

Calculate the area of the parallelogram according to the data in the diagram.

101010777AAABBBCCCDDDEEE

2

Step-by-step solution

We know that ABCD is a parallelogram. According to the properties of parallelograms, each pair of opposite sides are equal and parallel.

Therefore: CD=AB=10 CD=AB=10

We will calculate the area of the parallelogram using the formula of side multiplied by the height drawn from that side, so the area of the parallelogram is equal to:

SABCD=10×7=70cm2 S_{ABCD}=10\times7=70cm^2

3

Final Answer

70

Key Points to Remember

Essential concepts to master this topic
  • Formula: Area equals base times perpendicular height
  • Technique: Use Area = base × height = 10 × 7 = 70
  • Check: Height must be perpendicular to the base line ✓

Common Mistakes

Avoid these frequent errors
  • Using a slanted side instead of perpendicular height
    Don't measure the slanted side length as height = wrong area calculation! The slanted side is longer than the perpendicular distance. Always use the perpendicular height (shortest distance between parallel sides).

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 side length?

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Height is the perpendicular distance between parallel sides, while side length is the actual length of the parallelogram's edge. Height is usually shorter and forms a 90° angle with the base.

How do I identify the base and height from a diagram?

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The base can be any side of the parallelogram. The height is shown as a dashed line perpendicular to that base, often marked with a small square symbol at the corner.

Can I use any side as the base?

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Yes! You can use any side as the base, but you must use the corresponding perpendicular height to that specific side. Different bases will have different heights.

Why is the area 70 and not 17?

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Area = base × height = 10 × 7 = 70. The number 17 would come from adding base and height (10 + 7 = 17), but area requires multiplication, not addition.

Does it matter which units I use?

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Always use the same units for both measurements. If base is in cm and height is in cm, your area will be in cm². The diagram shows both measurements are 10 and 7 (same units).

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