How to Determine a Triangle and Circle of Equal Area

Two Methods:METHOD 1: The TutorialMETHOD 2: The Tutorial

Perhaps you are an artist or interior designer or architect, or perhaps you are into geometry as a discipline of logic. Here are two ways to determine a triangle and circle of equal area.

Steps

  • Become familiar with the basic image to be created:

Method 1
METHOD 1: The Tutorial

  • Image titled Determine a Triangle and Circle of Equal Area Step 2
  1. Image titled Determine a Triangle and Circle of Equal Area Step 3
    1
    Recall that the area of a triangle, TA, is determined by the formula TA = 1/2*b*h, where b= the base of the triangle and h= its height.
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    Recall that the area of a circle, CA, is determined by the formula CA = π*r^2, where π= PI() in Excel and r^2 = the radius of the circle squared.
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    Set these two formulas equal: 1/2*b*h = π*r^2, then
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    Exchange for the base (or height, but we'll use the base), the radius r of the circle, so that 1/2*r*h = π*r^2. In this case, the base of the triangle must equal the radius of the circle.
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    Solve for r: h/(2*π) = r^2 /r = r
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    Input the value for h and solve. Example: h=(2*π); (2*π)/(2*π) = 1 = r
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    TA = 1/2*r*h = 1/2*1*(2*π) = π; CA = π*r^2 = π*(1^2) = π. Done √

Method 2
METHOD 2: The Tutorial

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    1
    You are given the area for TA and must solve for CA .
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    Let TA = 18 such that 1/2*b*h = 1/2*6*6
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    Let CA = 18 = π*r^2
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    Let sqrt(18/π) = r = 2.394, then π*r^2 = 18.00521, which is probably close enough.
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    Or, you are given the area for CA and must solve for TA .
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    Let CA = π*r^2 = 1, then r = sqrt(1/π) = 0.56419 and π*r^2 = 1.00000147628531, which is probably close enough.
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    Let TA = 1/2*b*h = 1 or b*h = 2, and substitute in for b and h any values which make the equation valid and true. Done √

=== Helpful Guidance ===

  1. 1
    Make use of helper articles when proceeding through this tutorial:

Article Info

Categories: Calculating Volume and Area | Mathematics