Calculate Line Segment AF in Parallelogram ABCD with Given Measurements

Q: Why can a parallelogram have two different heights?

A parallelogram can use any side as a base, and each base has its own corresponding height (the perpendicular distance to the opposite side). The area stays the same no matter which base-height pair you use!

Q: How do I know which measurement is the height?

The height is always the perpendicular distance between parallel sides. In this problem, the 3 cm is the height from B perpendicular to side AD, while AF is the height from A perpendicular to side AB.

Q: What if I get confused about which sides are parallel?

In parallelogram ABCD, opposite sides are parallel: AB is parallel to DC and AD is parallel to BC. The height connects these parallel pairs at right angles.

Q: Can I use the side lengths directly as heights?

No! Side lengths (like AD = 4 cm) are not heights unless specifically stated. Heights are always perpendicular distances, which are usually different from side lengths in slanted parallelograms.

Q: How do I check if my answer makes sense?

Calculate the area using both base-height pairs: $ 6 \times 3 = 18 $ and $ 4 \times 4.5 = 18 $. If you get the same area both ways, your answer is correct!

Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:04 Let's find the length of A F.

00:07 Remember, in a parallelogram, opposite sides are equal.

00:16 We'll use the formula to calculate the area of a parallelogram.

00:21 Take side D C and multiply it by the height A E.

00:26 Let's substitute the values, then solve to find the area.

00:30 This gives us the area of the parallelogram.

00:35 Again, opposite sides are equal in a parallelogram.

00:41 Now, let's calculate the area using a different height.

00:46 We'll apply the formula again, this time with height A F.

00:57 Substitute the appropriate values to solve for A F.

01:14 And that's how we solve this problem!

Step-by-step written solution

Follow each step carefully to understand the complete solution

1

Understand the problem

Given the parallelogram ABCD

Find AF

2

Step-by-step solution

To solve this problem, we'll follow these steps:

Step 1: Identify the given dimensions and properties of parallelogram $ABCD$ .
Step 2: Calculate the area of the parallelogram using the known base and height.
Step 3: Use the area and other dimensions to determine the required segment $AF$ .

Now, let's work through each step:

Step 1: Parallelogram $ABCD$ has $AB = 6$ cm and $AD = 4$ cm. The height from $B$ opposite $AD$ is $3$ cm.

Step 2: Calculate the area with base $AB$ :

$\text{Area} = 6 \times 3 = 18$ square centimeters.

Step 3: Use base $AD$ to find $AF$ (height):

$18 = 4 \times AF$ .

Solve for $AF$ :

$AF = \frac{18}{4} = 4.5$ cm.

Therefore, the solution to the problem is $AF = 4.5$ cm.

3

Final Answer

$4.5$ cm

Key Points to Remember

Essential concepts to master this topic

Area Formula: Same parallelogram area using different base-height pairs
Technique: Use $Area = base \times height$ twice: 6 × 3 = 18
Check: Verify with second calculation: 4 × 4.5 = 18 ✓

Common Mistakes

Avoid these frequent errors

Using the wrong dimensions as base and height
Don't confuse side lengths with heights = wrong area calculation! The height must be perpendicular to the base, not just any side length. Always identify which measurement is the perpendicular distance.

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

Why can a parallelogram have two different heights?

+

A parallelogram can use any side as a base, and each base has its own corresponding height (the perpendicular distance to the opposite side). The area stays the same no matter which base-height pair you use!

How do I know which measurement is the height?

+

The height is always the perpendicular distance between parallel sides. In this problem, the 3 cm is the height from B perpendicular to side AD, while AF is the height from A perpendicular to side AB.

What if I get confused about which sides are parallel?

+

In parallelogram ABCD, opposite sides are parallel: AB is parallel to DC and AD is parallel to BC. The height connects these parallel pairs at right angles.

Can I use the side lengths directly as heights?

+

No! Side lengths (like AD = 4 cm) are not heights unless specifically stated. Heights are always perpendicular distances, which are usually different from side lengths in slanted parallelograms.

How do I check if my answer makes sense?

+

Calculate the area using both base-height pairs: $6 \times 3 = 18$ and $4 \times 4.5 = 18$ . If you get the same area both ways, your answer is correct!

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Parallelogram questions, detailed video solutions, and personalized progress tracking.

📹

Unlimited Video Solutions

Step-by-step explanations for every problem

📊

Progress Analytics

Track your mastery across all topics

🚫

Ad-Free Learning

Focus on math without distractions

No credit card required • Cancel anytime

Calculate Line Segment AF in Parallelogram ABCD with Given Measurements

Parallelogram Area with Multiple Height Applications

❤️ Continue Your Math Journey!

Step-by-step video solution

Step-by-step written solution

Understand the problem

Step-by-step solution

Final Answer

Key Points to Remember

Common Mistakes

Practice Quiz

FAQ

Why can a parallelogram have two different heights?

How do I know which measurement is the height?

What if I get confused about which sides are parallel?

Can I use the side lengths directly as heights?

How do I check if my answer makes sense?

🌟 Unlock Your Math Potential

More Questions

Area of a Parallelogram

Calculate X in the Parallelogram: Step-by-Step to Find Height BE

Calculate Length DF in Parallelogram ABCD: Given AB=12cm, ED=8cm, BC=10cm

Calculate Side Length DC in Parallelogram with Area 88 cm²

Calculate Side Length AE in a Parallelogram with Area 63 cm²

Parallelogram

Parallelogram Side Length: Finding DC Using Height 12 and Base Segment 5

Calculate DC Length in Parallelogram: Using AE/DC = 1/2 Ratio

Calculate Parallelogram Height AE: Given Area 82 cm² and Base 4 cm

Parallelogram Length Calculation: Finding BE in a 60 cm² Shape