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Three Methods:Helpful GuidanceMETHOD 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.

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Method 1 of 3: Helpful Guidance

  1. 1
    Make use of helper articles when proceeding through this tutorial:
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  2. 2

Method 2 of 3: METHOD 1: The Tutorial

  1. 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.
  2. 2
    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.
  3. 3
    Set these two formulas equal: 1/2*b*h = π*r^2, then
  4. 4
    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.
  5. 5
    Solve for r: h/(2*π) = r^2 /r = r
  6. 6
    Input the value for h and solve. Example: h=(2*π); (2*π)/(2*π) = 1 = r
  7. 7
    TA = 1/2*r*h = 1/2*1*(2*π) = π; CA = π*r^2 = π*(1^2) = π. Done √

Method 3 of 3: METHOD 2: The Tutorial

  1. 1
    You are given the area for TA and must solve for CA .
  2. 2
    Let TA = 18 such that 1/2*b*h = 1/2*6*6
  3. 3
    Let CA = 18 = π*r^2
  4. 4
    Let sqrt(18/π) = r = 2.394, then π*r^2 = 18.00521, which is probably close enough.
  5. 5
    Or, you are given the area for CA and must solve for TA .
  6. 6
    Let CA = π*r^2 = 1, then r = sqrt(1/π) = 0.56419 and π*r^2 = 1.00000147628531, which is probably close enough.
  7. 7
    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 √
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Article Info

Categories: Calculating Volume and Area | Mathematics

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