# Equilateral Triangle

Discussion in 'Other Pre-University Math' started by nycmathguy, Nov 1, 2021.

1. ### nycmathguy

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Set 6.1
David Cohen

nycmathguy, Nov 1, 2021
2. ### MathLover1

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49.
show that area of an equaterial triangle of side s is given by

(sqrt(3)/4)s^2

Area of Triangle = 1/2* base * height

Here, base = s, and height = h

Now, apply Pythagoras Theorem in the triangle.

s^2 = h^2 + (s/2)^2

h^2 = s^2 – (s^2/4)

h^2 = (3s^2)/4

Or, h = (1/2)(√3*s)

Now, put the value of “h” in the area of the triangle equation.

A =1/2* s * (1/2)(√3*s)

Or, Area of Equilateral Triangle = (√3/4)*s^2

50.
show that the area of the shaded segment is given by

s^2((2pi-3sqrt(3))/12)

the area of the shaded segment= the area of the circle sector ABC- the area of the triangle ABC

the area of the circle sector ABC=(theta/360)*pi*r^2

central angle theta=60 degrees, r=s

the area of the circle sector ABC=(60/360)*pi*s^2=(1/6)pi*s^2

use the area of the triangle ABC from 49 which is = (√3/4)*s^2

then

the area of the shaded segment=(1/6)pi*s^2- (√3/4)*s^2
the area of the shaded segment=(2pi/12)*s^2- (3√3)/12*s^2
the area of the shaded segment=(2pi- 3√3)/12*s^2

MathLover1, Nov 1, 2021
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3. ### nycmathguy

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I hope you don't mind the occasional David Cohen textbook questions. David's textbook is a lot more involved than the Ron Larson book. I just love the Cohen textbook questions which are above my current level of mathematics.

nycmathguy, Nov 1, 2021
4. ### MathLover1

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I don't mind , both textbooks are good

MathLover1, Nov 2, 2021
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