# Isosceles Triangles Calculator

## 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

*h*a = *h*c

K = area

P = perimeter

See Diagram Below:

*h*a = altitude of a

*h*b = altitude of b

*h*c = 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.

## Calculator Use

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: *h*a, *h*b, and *h*c. 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:
*h*a =*h*c - 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) * √(4a
^{2}- b^{2}) - Altitude a of Isosceles Triangle:
*h*a = (b/2a) * √(4a^{2}- b^{2}) - Altitude b of Isosceles Triangle:
*h*b = (1/2) * √(4a^{2}- b^{2}) - Altitude c of Isosceles Triangle:
*h*c = (b/2a) * √(4a^{2}- b^{2})

### 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,
*h*a,*h*b, and*h*c - c = a
- P = 2a + b
- s = a + (b/2)
- K = (b/4) * √(4a
^{2}- b^{2}) *h*a = (b/2a) * √(4a^{2}- b^{2})*h*b = (1/2) * √(4a^{2}- b^{2})*h*c = (b/2a) * √(4a^{2}- b^{2})

For more information on right triangles see:

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

**Cite this content, page or calculator as:**

Furey, Edward "Isosceles Triangles Calculator"; from *https://www.calculatorsoup.com* - Online Calculator Resource.