Calculate Parallelogram Area: Using Circle Diameter 10π cm and Rhombus Area 24 cm²

Q: Why can't I use the circle information to find the area?

The circle gives us BC = 5 cm, but to find area using $ \text{Area} = BC \times h $, we need the perpendicular height from BC to AD, which isn't provided.

Q: How do I recognize when there's insufficient information?

Check each formula:Area = base × height (need both base AND height)Area = side₁ × side₂ × sin(angle) (need two sides AND included angle)If any required element is missing, the problem cannot be solved.

Q: What should I do when information is insufficient?

State clearly: "It is not possible to calculate" and explain what additional information would be needed. This shows mathematical reasoning, not failure!

Q: Could the diagram provide missing measurements?

Always examine diagrams carefully, but in this case, no perpendicular heights or angle measurements are marked that would allow area calculation.

Insufficient Information with Area Problems

The parallelogram ABCD is shown below.

BC is the diameter of the circle whose circumference is equal to $10\pi$ cm.

ECFD is a rhombus whose area is 24 cm².

What is the area of ABCD?

❤️ 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

00:14 Let's find the area of parallelogram, A, B, C, D.

00:18 We'll use the formula for the area of a parallelogram.

00:22 Multiply side D, C by height, H.

00:26 Let's draw height H to meet side D, C.

00:33 But we don't know height, H, for side D, C.

00:40 Now, let's try using side B, C.

00:45 Draw height H to meet side B, C.

00:53 We still don't know height, H, here either.

00:56 So, we can't solve this problem, yet.

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

The parallelogram ABCD is shown below.

BC is the diameter of the circle whose circumference is equal to $10\pi$ cm.

ECFD is a rhombus whose area is 24 cm².

What is the area of ABCD?

Step-by-step solution

Let's try to calculate the area in two ways.

In the first method, we will try to use the rhombus ECFD:

Let's try to calculate according to the formula $area=DC\times h_{DC}$

We will lower a height to DC and see that we do not have enough data to calculate, so we will not be able to calculate the area of the parallelogram using the rhombus.

In the second method , we will try to use the circle:

$area=BC\times h_{BC}$ We will lower a height to BC and see that we do not have enough data to calculate, so we will not be able to calculate the area of the parallelogram using the circle.

From this it follows that we do not have enough data to calculate the area of parallelogram ABCD and therefore the exercise cannot be solved.

Final Answer

It is not possible to calculate.

Key Points to Remember

Essential concepts to master this topic

Given Data Analysis: Circle diameter 5 cm, rhombus area 24 cm²
Height Method: Area = base × height requires perpendicular distance
Verification: Check if all necessary measurements are provided ✓

Common Mistakes

Avoid these frequent errors

Assuming you can always solve with given information
Don't automatically try formulas just because some measurements are given = wrong calculations! Missing the height between parallel sides makes area calculation impossible. Always identify what specific measurements are needed for each formula.

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.

FAQ

Everything you need to know about this question

Why can't I use the circle information to find the area?

The circle gives us BC = 5 cm, but to find area using $\text{Area} = BC \times h$ , we need the perpendicular height from BC to AD, which isn't provided.

What about using the rhombus area of 24 cm²?

The rhombus ECFD has area 24 cm², but this doesn't tell us the height of parallelogram ABCD. We'd need to know how the rhombus relates to the parallelogram's dimensions.

How do I recognize when there's insufficient information?

Check each formula:

Area = base × height (need both base AND height)
Area = side₁ × side₂ × sin(angle) (need two sides AND included angle)

If any required element is missing, the problem cannot be solved.

What should I do when information is insufficient?

State clearly: "It is not possible to calculate" and explain what additional information would be needed. This shows mathematical reasoning, not failure!

Could the diagram provide missing measurements?

Always examine diagrams carefully, but in this case, no perpendicular heights or angle measurements are marked that would allow area calculation.

🌟 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 Parallelogram Area: Using Circle Diameter 10π cm and Rhombus Area 24 cm²

Insufficient Information with Area Problems

❤️ 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't I use the circle information to find the area?

What about using the rhombus area of 24 cm²?

How do I recognize when there's insufficient information?

What should I do when information is insufficient?

Could the diagram provide missing measurements?

🌟 Unlock Your Math Potential

More Questions

Parallelogram

Parallelogram Problem: Finding Side AD When Area = 40 cm² and Height = 4 cm

Calculate Parallelogram Height AE Using Area = 40 cm² and Base = 8 units

Calculate Parallelogram Side Length: Area 100 cm² with Height 6

Calculate Side Length DC in a Parallelogram with Area 70 cm²

Area of a Parallelogram

Calculate Side Length AB in a Parallelogram with Area 156 cm² and Height 12

Parallelogram Length Calculation: Finding BE in a 60 cm² Shape

Calculate Parallelogram Perimeter: Given Area 75 cm² and Height 5 units

Calculate Parallelogram Area: Given Perimeter 47cm and Height 6