Calculate Parallelogram Height: Area 60 cm² with 8 cm Base

Q: How do I know which side is the base?

The base is usually the side that's labeled with a measurement and lies along the bottom. In this problem, AD = 8 cm is clearly marked as the base of the parallelogram.

Q: What's the difference between a side length and height?

A side length is the actual distance along the edge of the parallelogram. The height is the perpendicular distance between parallel sides - it's always measured at a 90° angle to the base.

Q: Why isn't the height just 8 cm like the base?

In parallelograms, the height is rarely the same as the side length unless it's a rectangle. The height is always the perpendicular distance, which is usually different from the slanted side length.

Q: How do I check if 7.5 cm is reasonable?

Ask yourself: does 8 × 7.5 = 60? Yes! Also, since the parallelogram looks slanted in the diagram, it makes sense that the height (7.5) is less than the base (8).

Area Formula with Missing Height

Look at the parallelogram ABCD.

The area ABCD is 60 cm².
$AD=8$

Calculate the height of ABCD.

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Find the height of the parallelogram

00:03 We'll use the formula for calculating the area of a parallelogram (side times height)

00:10 We'll substitute appropriate values according to the given data and solve for the height

00:14 We'll isolate the height

00:18 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Look at the parallelogram ABCD.

The area ABCD is 60 cm².
$AD=8$

Calculate the height of ABCD.

Step-by-step solution

To solve this problem, we need to calculate the height of parallelogram ABCD using the area formula for parallelograms:

Step 1: Recall the formula $\text{Area} = \text{base} \times \text{height}$ .
Step 2: Substitute the known values into the formula: $60 = 8 \times \text{height}$ .
Step 3: Rearrange the formula to solve for height: $\text{height} = \frac{60}{8}$ .
Step 4: Perform the division to find the height: $\text{height} = 7.5$ cm.

Therefore, the height of parallelogram ABCD is $7.5$ cm.

Final Answer

7.5

Key Points to Remember

Essential concepts to master this topic

Formula: Area of parallelogram equals base times height
Technique: Rearrange to height = Area ÷ base = 60 ÷ 8
Check: Verify 8 × 7.5 = 60 cm² matches given area ✓

Common Mistakes

Avoid these frequent errors

Confusing base with height measurements
Don't use AD = 8 as the height when it's labeled as the base! This gives Area = height × 8, making height = 60 ÷ height, which is circular. Always identify which measurement is the base from the diagram and labels.

Practice Quiz

Test your knowledge with interactive questions

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

FAQ

Everything you need to know about this question

How do I know which side is the base?

The base is usually the side that's labeled with a measurement and lies along the bottom. In this problem, AD = 8 cm is clearly marked as the base of the parallelogram.

What's the difference between a side length and height?

A side length is the actual distance along the edge of the parallelogram. The height is the perpendicular distance between parallel sides - it's always measured at a 90° angle to the base.

Why isn't the height just 8 cm like the base?

In parallelograms, the height is rarely the same as the side length unless it's a rectangle. The height is always the perpendicular distance, which is usually different from the slanted side length.

Can I use a different side as the base?

Yes! You can use any side as the base, but then you need the corresponding height (perpendicular to that base). The area will always be the same: base × height = 60 cm².

How do I check if 7.5 cm is reasonable?

Ask yourself: does 8 × 7.5 = 60? Yes! Also, since the parallelogram looks slanted in the diagram, it makes sense that the height (7.5) is less than the base (8).

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