# 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.

### Method 1 METHOD 1: The Tutorial

- 1
**Recall that the area of a triangle, T**_{A}, is determined by the formula T_{A}= 1/2*b*h, where b= the base of the triangle and h= its height. - 2
**Recall that the area of a circle, C**_{A}, is determined by the formula C_{A}= π*r^2, where π= PI() in Excel and r^2 = the radius of the circle squared. - 3
**Set these two formulas equal:**1/2*b*h = π*r^2, then - 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
**Solve for r:**h/(2*π) = r^2 /r = r - 6
**Input the value for h and solve.**Example: h=(2*π); (2*π)/(2*π) = 1 = r - 7
**T**Done √_{A}= 1/2*r*h = 1/2*1*(2*π) = π; C_{A}= π*r^2 = π*(1^2) = π.

### Method 2 METHOD 2: The Tutorial

- 1
**You are given the area for T**_{A}and must solve for C_{A}. - 2
**Let T**_{A}= 18 such that 1/2*b*h = 1/2*6*6 - 3
**Let C**_{A}= 18 = π*r^2 - 4
**Let sqrt(18/π) = r = 2.394, then π*r^2 = 18.00521, which is probably close enough.** - 5
**Or, you are given the area for C**_{A}and must solve for T_{A}. - 6
**Let C**_{A}= π*r^2 = 1, then r = sqrt(1/π) = 0.56419 and π*r^2 = 1.00000147628531, which is probably close enough. - 7
**Let**Done √**T**= 1/2*b*h = 1 or_{A}**b*h = 2**, and substitute in for b and h any values which make the equation valid and true.

=== Helpful Guidance ===

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**Make use of helper articles when proceeding through this tutorial:**- See the article How to Determine a Square and Circle of Equal Perimeter for a list of articles related to Excel, Geometric and/or Trigonometric Art, Charting/Diagramming and Algebraic Formulation.
- For more art charts and graphs, you might also want to click on Category:Microsoft Excel Imagery, Category:Mathematics, Category:Spreadsheets or Category:Graphics to view many Excel worksheets and charts where Trigonometry, Geometry and Calculus have been turned into Art, or simply click on the category as appears in the upper right white portion of this page, or at the bottom left of the page.

## Article Info

Categories: Calculating Volume and Area | Mathematics