Chapter 29: Chapter 29

Problem 550

A circle is inscribed in an equilateral triangle, whose side is 12\. Find, to the nearest integer, the difference between the area of the triangle and the area of the circle. (Use \(\pi=3.14\) and \(\sqrt{3}=1.73 .\) )

Short Answer

Expert verified

The area of the equilateral triangle is approximately 72.03, and the area of the inscribed circle is approximately 37.81. The difference between the areas is about 34.22, which, when rounded to the nearest integer, is 34.

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Step by step solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Step 1: Find the area of the equilateral triangle

Using the formula for the area of the equilateral triangle, we have: Area = \(\frac{\sqrt{3}}{4} \times 12^2 = \frac{\sqrt{3}}{4} \times 144\) Since \(\sqrt{3} = 1.73\), we can substitute the value: Area = \(\frac{1.73}{4} \times 144 \approx 72.03\)

Step 2: Find the radius of the inscribed circle

Using the formula for the radius of the inscribed circle, we have: Radius = \(\frac{12}{2\sqrt{3}} = \frac{12}{2 \times 1.73}\) Radius = \(3.47\), rounding to two decimal places

Step 3: Find the area of the inscribed circle

Using the formula for the area of a circle, we have: Area = \(\pi \times (3.47)^2\) Since \(\pi = 3.14\), we can substitute the value: Area = \(3.14 \times 12.04 \approx 37.81\)

Step 4: Find the difference between the areas and round to the nearest integer

Now that we have both areas, we can calculate the difference: Difference = Area of triangle - Area of circle Difference = \(72.03 - 37.81 \approx 34.22\) To round to the nearest integer, the difference is: Difference = \(34\).

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Chapter 29: Chapter 29

A circle is inscribed in an equilateral triangle, whose side is 12\. Find, to the nearest integer, the difference between the area of the triangle and the area of the circle. (Use \(\pi=3.14\) and \(\sqrt{3}=1.73 .\) )

Short Answer

Step by step solution

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Step 1: Find the area of the equilateral triangle

Step 2: Find the radius of the inscribed circle

Step 3: Find the area of the inscribed circle

Step 4: Find the difference between the areas and round to the nearest integer

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Chapter 1

Chapter 2

Chapter 3

Chapter 4

Chapter 5

Chapter 6

Chapter 7

Chapter 8

Chapter 9

Chapter 10

Chapter 11

Chapter 12

Chapter 13

Chapter 14

Chapter 15

Chapter 16

Chapter 17

Chapter 18

Chapter 19

Chapter 20

Chapter 21

Chapter 22

Chapter 23

Chapter 24

Chapter 25

Chapter 26

Chapter 27

Chapter 28

Chapter 30

Chapter 31

Chapter 32

Chapter 33

Chapter 34

Chapter 35

Chapter 36

Chapter 37

Chapter 38

Chapter 39

Chapter 40

Chapter 41

Chapter 42

Chapter 43

Chapter 44

Chapter 48

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Chapter 51

Chapter 52

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