This calculator computes parameters of triangles where each side is equal and each angle is exactly 60 degrees. Inputting any value into any of the slots yields output in every other slot. The values are…
•a - The edge measure of any side.
•h - As the triangle is horizontally on its base, this gives the height.
•Area - The area of the triangle's face.
• Perimeter - The total sum of the three sides.
• Circumcircle radius - The radius of the smallest possible circle that can fit outside the triangle.
• Incircle radius - The radius of the largest possible circle that will fir inside the triangle.
An equilateral triangle is a regular geometric shape in which all three sides are congruent, and the angle bisectors, perpendicular bisectors, and medians all coincide.
The height is often computed because it's a shortcut to using the Pythagorean theorem to compute some of its parameters. Every equilateral triangle can be sliced down the middle into two 30-60-90 right triangles, making for a handy application of the hypotenuse formula.
The calculator of course also offers measurement units in imperial and metric, which work independently in case you have to convert units at the same time.
Figuring the equilateral triangle is a straightforward set of known equations, giving A as a side measure:
•Perimeter = A * 3•Height = A * (√3 / 2)•Area = (A ^ 2) * (√3 / 4)•Circumscribed circle radius = A / √3•Inscribed circle radius = A * (√3 / 6)
One can easily see where the triangle, split into two 30-60-90 triangles, can have those two combined into one rectangle of the measure (A * (√3 / 2)) x (A / 2). An equilateral triangle of length A = 3 can be reconstructed into a rectangle 2.6 x 1.5.
The ancient Greek philosophers held perfect geometric shapes and solids as sacred, constructed by the gods, and one can imagine they were inspired by the equilateral triangle. It is a tessellating shape, which means that an infinite number of them can be packed into a plane without wasted space. The Dutch artist M.C. Escher is famous for his geometric images which incorporate triangle tessellations into abstract fields of nesting shapes. In three dimensions, four equilateral triangles folded together form a tetrahedron, the smallest Platonic solid.
An equilateral triangle is also easily constructed using only a compass and straightedge, and the proof of this was the very first entry in Euclid's first book of Elements.