Calculate Parallelogram Area: Circle with Circumference 25.13 and Tangent Points

Q: Why are the tangent segments from each vertex equal?

This is a fundamental tangent property! When two tangent lines are drawn from the same external point to a circle, the segments are always equal. So from point A: AE = AF = 3, and from point B: BG = BF = 6.

Q: How do I find the parallelogram's height from the circle?

The height equals the diameter of the inscribed circle! Since all sides are tangent to the circle, the distance between parallel sides equals the diameter = 2r.

Q: How do I get radius 4 from circumference 25.13?

Use the circumference formula: $ C = 2\pi r $$ 25.13 = 2\pi r $$ r = \frac{25.13}{2\pi} \approx \frac{25.13}{6.28} \approx 4 $

Q: What if the parallelogram isn't drawn to scale?

Always rely on the given measurements, not the visual appearance! Use the tangent lengths (3 and 6) and circumference (25.13) to calculate, regardless of how the diagram looks.

Tangent Parallelogram Area with Circle Properties

Below is a circle bounded by a parallelogram:

All meeting points are tangential to the circle.
The circumference is 25.13.

What is the area of the parallelogram?

❤️ 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

00:11 Let's find the area of the parallelogram.

00:15 Lines starting from the same point are equal until they meet.

00:24 A side is equal to the sum of its parts.

00:34 Draw a diameter in the circle.

00:39 The radius is always at a right angle to the tangent where they meet.

00:44 We'll use the circle's circumference formula to find the radius.

00:49 Let's substitute the values and find the radius.

00:58 Round this radius. Now we know the radius and diameter!

01:05 To get the area, multiply the height, E H, by the side, A B.

01:11 Substitute the values and solve for the area.

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

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Below is a circle bounded by a parallelogram:

All meeting points are tangential to the circle.
The circumference is 25.13.

What is the area of the parallelogram?

Step-by-step solution

First, we add letters as reference points:

Let's observe points A and B.

We know that two tangent lines to a circle that start from the same point are parallel to each other.

Therefore:

$AE=AF=3$
$BG=BF=6$

And from here we can calculate:

$AB=AF+FB=3+6=9$

Now we need the height of the parallelogram.

We know that F is tangent to the circle, so the diameter that comes out of point F will also be the height of the parallelogram.

It is also known that the diameter is equal to two radii.

Since the circumference is 25.13.

Circumference formula: $2\pi R$
We replace and solve:

$2\pi R=25.13$
$\pi R=12.565$
$R\approx4$

The height of the parallelogram is equal to two radii, that is, 8.

And from here you can calculate with a parallelogram area formula:

$AlturaXLado$

$9\times8\approx72$

Final Answer

$\approx72$

Key Points to Remember

Essential concepts to master this topic

Tangent Property: Equal tangent segments from external point to circle
Technique: Use $C = 2\pi r$ to find radius from circumference 25.13
Check: Diameter equals height, area = base × height = 9 × 8 = 72 ✓

Common Mistakes

Avoid these frequent errors

Using circumference as diameter
Don't use circumference 25.13 directly as the diameter = area of 226! The circumference must be divided by π to get diameter. Always use C = 2πr to find radius first, then diameter = 2r.

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 are the tangent segments from each vertex equal?

This is a fundamental tangent property! When two tangent lines are drawn from the same external point to a circle, the segments are always equal. So from point A: AE = AF = 3, and from point B: BG = BF = 6.

How do I find the parallelogram's height from the circle?

The height equals the diameter of the inscribed circle! Since all sides are tangent to the circle, the distance between parallel sides equals the diameter = 2r.

Why is the base length 3 + 6 = 9?

The base AB consists of two tangent segments: AF = 3 and FB = 6. Since these segments are adjacent on the same side, we add them: AB = AF + FB = 3 + 6 = 9.

How do I get radius 4 from circumference 25.13?

Use the circumference formula: $C = 2\pi r$
$25.13 = 2\pi r$
$r = \frac{25.13}{2\pi} \approx \frac{25.13}{6.28} \approx 4$

What if the parallelogram isn't drawn to scale?

Always rely on the given measurements, not the visual appearance! Use the tangent lengths (3 and 6) and circumference (25.13) to calculate, regardless of how the diagram looks.

🌟 Unlock Your Math Potential

Get unlimited access to all 18 Circle 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: Circle with Circumference 25.13 and Tangent Points

Tangent Parallelogram Area with Circle Properties

❤️ 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 are the tangent segments from each vertex equal?

How do I find the parallelogram's height from the circle?

Why is the base length 3 + 6 = 9?

How do I get radius 4 from circumference 25.13?

What if the parallelogram isn't drawn to scale?

🌟 Unlock Your Math Potential

More Questions

Circle

Circle-Parallelogram Tangency Problem: Finding Area of Blue Regions with 25.13 Circumference

Calculate Circle Circumference: Finding the Distance Around a Circle with Radius 4

Parallelogram

Calculate Parallelogram Area: ABCD with Intersecting Deltoid BFCE

Calculate Parallelogram Area: 4cm Height × 7cm Base Problem

Calculate Parallelogram Area: Rectangle with Perimeter 24 Inside

Parallelogram Area Calculation: Using Height CE and Segments 5, 7, and 2

Area of a Parallelogram

Calculate Parallelogram Area Using Exterior Height: 10-Unit Height Problem

Calculate Parallelogram Area with Height 3 and Side Length 8

Calculate Parallelogram Area: 6cm Base and 2cm Height Problem

Calculate Parallelogram Area: 7 cm Base with 3.5 cm Height

Circumference

Calculate Trapezoid Area with 7π Segment and Semicircle: Step-by-Step Solution

Calculate Circle Area When Rectangle Area = 28X: Geometric Relationship Problem

Calculate Circle Circumference: Using Given Radius Length of 8

Calculate Circle Perimeter: Given Radius = 4 Units