How this calculator works
Draw an altitude in an equilateral triangle. It splits the 60° vertex into two 30° angles, halves the base and leaves a right angle at the foot. Thus the original equilateral side becomes twice the short leg. Pythagoras gives the remaining leg as √3 times the short leg. The extra altitude and radii help when this triangle sits inside a larger construction.
Formula
a:b:c=1:√3:2; K=√3 a²/2; P=(3+√3)a; h to c=√3 a/2; R=c/2=a; r=(a+b-c)/2.
Worked example
If the short leg is 4 cm, the long leg is 4√3 cm, the hypotenuse is 8 cm and the area is 8√3 cm². A hypotenuse of 10 m instead gives legs 5 m and 5√3 m.
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Frequently asked questions
Which side is half the hypotenuse?
The side opposite 30°. It is the short leg a, not the leg opposite 60°.
How do I recover a from area?
Divide twice the area by √3, then take the positive square root. The area input must use square units.
Is this the same shape as half a square?
No. Half a square has angles 45°, 45° and 90°. This triangle comes from half an equilateral triangle.