Geometry problems can stress anyone out, given how many complexities there are. That’s why you may see the value in using an isosceles triangle calculator. This tool can calculate heights, angles, perimeters and other parameters of an isosceles triangle.
You might not think such a tool is valuable if all it can measure is one specific kind of triangle. However, consider how many things form that shape. A dog’s kennel, the angle of a roof, steeples, arrowheads, the list goes on. Whether you use an isosceles triangle in mathematics class or real life, this is the tool for you. Find out about isosceles triangle formulas and more below.
What is an Isosceles Triangle?
An isosceles triangle has two equal sides (legs), and a third side, the base. The angle between the two legs is the vertex, and the angles by the base are called base angles.
An isosceles has quite a complicated list of properties. Along the vertex height is the axis of symmetry. The two angles opposite its legs are the same length. An isosceles triangle can also be obtuse, right, or acute. The determining factor for this is the vertex angle. A base angle, for example, is always acute. The only exception is for an equilateral triangle, which is also considered an isosceles triangle.
Working Out Perimeter and Area with Isosceles Triangle Formulas
There are multiple ways to calculate this triangle’s perimeter and area. Below, we list the most popular methods.
Calculating an isosceles triangle area:
1. When you have arm ‘a’ and base ‘b’
Area = (¼) x b x √ (4 x a² - b²)
2. When you have the height (h) from the apex and base (b), or height from the two vertices and arm ‘a’
Area = 0.5 x h x b x 0.5 x h2 x a
3. When you have an angle and a base or arm
Area = (1/2) x a x b x sin (base angle) = (1/2) x a² x sin (vertex angle)
Did you know you can also use a triangle area calculator to work out all triangle type areas?
Calculating an isosceles triangle perimeter:
1. Add all the sides
Perimeter = a + a + b = 2 x a + b
The Isosceles Triangle Theorem
When a triangle's two sides are congruent, so are the opposite angles. That's the isosceles triangle theorem. The same rules apply when you reverse the rule.
The Golden Triangle Calculator
A sublime or golden triangle, is an isosceles triangle with a leg containing a golden ratio.
a / b = φ ~ 1.618
The golden triangle has three angles in a 2:2:1 proportion which you use to form a logarithmic spiral.
Find the Area of an Isosceles Triangles with our Tool
Using this calculator is far easier than working out the equations by hand. Follow these steps below.
1. Enter your first value. Let’s say you want to know a golden triangle’s properties. The leg box would need to have 1.681 inches.
2. Enter your second value. Let’s say your base is three inches.
3. The calculator works out everything else. You now know the area of the isosceles triangle is 0.93 inches-squared.