Calculators

Geometry

Plane

Isosceles Triangle Shape

A = angle A
a = side a
B = angle B
b = side b
C = angle C
c = side c

A = C
a = c
ha = hc

K = area
P = perimeter

See Diagram Below:
ha = altitude of a
hb = altitude of b
hc = altitude of c

*Length units are for your reference only since the value of the resulting lengths will always be the same no matter what the units are.

An isosceles triangle is a special case of a triangle where 2 sides, a and c, are equal and 2 angles, A and C, are equal.

In our calculations for a right triangle we only consider 2 known sides to calculate the other 7 unknowns. For example, if we know a and b we know c since c = a. Once we know sides a, b, and c we can calculate the perimeter = P, the semiperimeter = s, the area = K, and the altitudes: ha, hb, and hc. Let us know if you have any other suggestions!

Formulas and Calculations for an isosceles triangle:

• Sides of Isosceles Triangle: a = c
• Angles of Isosceles Triangle: A = C
• Altitudes of Isosceles Triangle: ha = hc
• Perimeter of Isosceles Triangle: P = a + b + c = 2a + b
• Semiperimeter of Isosceles Triangle: s = (a + b + c) / 2 = a + (b/2)
• Area of Isosceles Triangle: K = (b/4) * √(4a² - b²)
• Altitude a of Isosceles Triangle: ha = (b/2a) * √(4a² - b²)
• Altitude b of Isosceles Triangle: hb = (1/2) * √(4a² - b²)
• Altitude c of Isosceles Triangle: hc = (b/2a) * √(4a² - b²)

Calculation:
Given sides a and b find side c and the perimeter, semiperimeter, area and altitudes

• a and b are known; find c, P, s, K, ha, hb, and hc
• c = a
• P = 2a + b
• s = a + (b/2)
• K = (b/4) * √(4a² - b²)
• ha = (b/2a) * √(4a² - b²)
• hb = (1/2) * √(4a² - b²)
• hc = (b/2a) * √(4a² - b²)

For more information on right triangles see:

Weisstein, Eric W. "Isosceles Triangle." From MathWorld--A Wolfram Web Resource. Isosceles Triangle.