Chapter 11: Q19. (page 431)

Find the area of each figure:
A square inscribed in a circle with radiusr.

Short Answer

Expert verified

The area of given figure is $2 r^{2}$ square units.

Step by step solution

Step 1. Analyze the given information.

Let the side of the square is x and the radius of circle r ,

Then, $D B = r + r = 2 r$

Step 2. Concept Used.

We can use Pythagoras theorem.

Pythagorean Theorem define that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

In $△ B C D$

$D B^{2} = B C^{2} + C D^{2}$

${(2 r)}^{2} = x^{2} + x^{2}$

$2 x^{2} = 4 r^{2}$

$x^{2} = 2 r^{2}$

$x = \sqrt{2} r$

Thus, the side of square is $\sqrt{2} r$

Step 3. Find the area of given figure.

Area of square can be found using the formula

$A = s^{2}$

Where,

s= Side of square

$A = {(\sqrt{2} r)}^{2}$

$= 2 r^{2}$ Square units.

Therefore, the area of given figure is $2 r^{2}$ square units.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

Recommended explanations on Math Textbooks

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Find the area of each figure:
A square inscribed in a circle with radiusr.

Short Answer

Step by step solution

Step 1. Analyze the given information.

Step 2. Concept Used.

Step 3. Find the area of given figure.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Logic and Functions

Mechanics Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the area of each figure:A square inscribed in a circle with radiusr.

Short Answer

Step by step solution

Step 1. Analyze the given information.

Step 2. Concept Used.

Step 3. Find the area of given figure.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Probability and Statistics

Logic and Functions

Mechanics Maths

Discrete Mathematics

Applied Mathematics

Study anywhere. Anytime. Across all devices.

Find the area of each figure:
A square inscribed in a circle with radiusr.