Calculate Parallelogram Height: Area 24 cm², Perimeter 24 cm with Double-Length Side

Parallelogram Properties with Side Relationships

ABCD is a parallelogram whose perimeter is equal to 24 cm.

The side of the parallelogram is two times greater than the adjacent side (AB>AD).

CE is the height of the side AB

The area of the parallelogram is 24 cm².

Find the height of CE

AAABBBCCCDDDEEE

❤️ Continue Your Math Journey!

We have hundreds of course questions with personalized recommendations + Account 100% premium

Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:19 Let's start by finding the height C E.
00:22 Remember, the perimeter of a parallelogram is the sum of all its sides.
00:31 Also, opposite sides in a parallelogram are equal.
00:37 Here, side A B is twice as long as side B C.
00:43 Let's plug in the values we know and solve for B C.
00:55 Great! Now we know the length of side B C.
00:59 Next, we'll use the B C value to find A B.
01:08 To find height C E, we'll do some more calculations.
01:11 Let's substitute the right values and solve for E C.
01:16 And that's how we solve the problem! Great job.

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

ABCD is a parallelogram whose perimeter is equal to 24 cm.

The side of the parallelogram is two times greater than the adjacent side (AB>AD).

CE is the height of the side AB

The area of the parallelogram is 24 cm².

Find the height of CE

AAABBBCCCDDDEEE

2

Step-by-step solution

The perimeter of the parallelogram is calculated as follows:

SABCD=AB+BC+CD+DA S_{ABCD}=AB+BC+CD+DA Since ABCD is a parallelogram, each pair of opposite sides is equal, and therefore, AB=DC and AD=BC

According to the figure that the side of the parallelogram is 2 times larger than the side adjacent to it, it can be argued thatAB=DC=2BC AB=DC=2BC

We inut the data we know in the formula to calculate the perimeter:

PABCD=2BC+BC+2BC+BC P_{ABCD}=2BC+BC+2BC+BC

We replace the given perimeter in the formula and add up all the BC coefficients accordingly:

24=6BC 24=6BC

We divide the two sections by 6

24:6=6BC:6 24:6=6BC:6

BC=4 BC=4

We know thatAB=DC=2BC AB=DC=2BC We replace the data we obtained (BC=4)

AB=DC=2×4=8 AB=DC=2\times4=8

As ABCD is a parallelogram, then all pairs of opposite sides are equal, therefore BC=AD=4

To find EC we use the formula:AABCD=AB×EC A_{ABCD}=AB\times EC

We replace the existing data:

24=8×EC 24=8\times EC

We divide the two sections by 824:8=8EC:8 24:8=8EC:8

3=EC 3=EC

3

Final Answer

3 cm

Key Points to Remember

Essential concepts to master this topic
  • Perimeter Formula: In parallelograms, opposite sides are equal: P = 2(a + b)
  • Side Relationship: If AB = 2×AD, then 24 = 2(2x + x) = 6x, so x = 4
  • Area Check: Verify height using Area = base × height: 24 = 8 × 3 ✓

Common Mistakes

Avoid these frequent errors
  • Treating all four sides as different lengths
    Don't use AB + BC + CD + DA = 24 with four different variables = overcomplicated system! This ignores that opposite sides in parallelograms are equal. Always remember AB = DC and AD = BC, so use P = 2(AB + AD).

Practice Quiz

Test your knowledge with interactive questions

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

101010777AAABBBCCCDDDEEE

FAQ

Everything you need to know about this question

Why are opposite sides equal in a parallelogram?

+

By definition, a parallelogram has opposite sides that are both parallel and equal in length. This is what makes it a parallelogram!

What does 'AB is two times greater than AD' mean exactly?

+

This means AB=2×AD AB = 2 \times AD . If we call AD = x, then AB = 2x. So one side is twice as long as the adjacent side.

How do I find the height when I know the area and base?

+

Use the formula Area=base×height \text{Area} = \text{base} \times \text{height} . Rearrange to get height=Areabase \text{height} = \frac{\text{Area}}{\text{base}} . Here: CE=248=3 CE = \frac{24}{8} = 3 cm.

Why is the height perpendicular to the base?

+

The height of a parallelogram is always the perpendicular distance between parallel sides. This gives the shortest distance and is needed for the correct area calculation.

Could I use a different side as the base?

+

Yes! You could use AD = 4 cm as the base. Then the height would be 244=6 \frac{24}{4} = 6 cm. The area stays the same: 24 cm².

🌟 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

More Questions

Click on any question to see the complete solution with step-by-step explanations