Calculate Parallelogram Area: Finding Expression with Base 13 and Height 4a

Area Formulas with Variable Expressions

Look at the parallelogram in the figure below.

Express its area in terms of a.

1313134a4a4aAAABBBCCCDDDEEE

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Express the area of the parallelogram using A
00:03 Calculate the area of the parallelogram using height(AE) multiplied by side(DC)
00:10 Substitute appropriate values and solve to find the area
00:19 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

Look at the parallelogram in the figure below.

Express its area in terms of a.

1313134a4a4aAAABBBCCCDDDEEE

2

Step-by-step solution

To find the area of the given parallelogram, we apply the formula for the area of a parallelogram, which is:

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

Here, the base is given as 1313 cm and the height is given as 4a4a.

Plugging these values into the formula, we have:

Area=13×4a\text{Area} = 13 \times 4a

Simplifying this, we get:

Area=52a\text{Area} = 52a

Therefore, the area of the parallelogram, expressed in terms of aa, is 52a\boxed{52a} cm².

The correct choice from the given options is therefore choice 3: 52a52a cm².

3

Final Answer

52a 52a cm²

Key Points to Remember

Essential concepts to master this topic
  • Formula: Parallelogram area equals base times height
  • Calculation: Multiply 13 × 4a to get 52a
  • Check: Units remain cm² and variable a stays in expression ✓

Common Mistakes

Avoid these frequent errors
  • Adding base and height instead of multiplying
    Don't add 13 + 4a = (13 + 4a) cm²! This gives a completely wrong formula and incorrect units. Always multiply base × height for parallelogram area.

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 don't I need to know the value of 'a' to solve this?

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The question asks for the area in terms of a, meaning your final answer should still contain the variable. You're finding an expression, not a specific number!

How do I know which measurement is the base and which is the height?

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In a parallelogram, the height is always perpendicular to the base. Look for the right angle symbol (small square) in the diagram - that shows the height measurement.

What if I get confused about which sides to use?

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Remember: use the base and height, not just any two sides! The height is the perpendicular distance between parallel sides, shown by the vertical line in the diagram.

Can I simplify 52a any further?

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No, 52a 52a is already in its simplest form. Since 52 and the variable a have no common factors to cancel, this is your final answer.

Why is the answer 52a cm² and not just 52a?

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Always include units in your final answer! Since both measurements were in cm, the area is in cm². The variable a represents a number, so the full answer is 52a cm².

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