The two equal sides are called the legs and have length a a. What is an isosceles triangle An isosceles triangle is a triangle with two equal sides. Let's start with the trigonometric triangle area formula:Īrea = (1/2) × a × b × sin(γ), where γ is the angle between the sides. The isosceles triangle area calculator can also work backward enter the area and some of the side lengths, and the calculator will work out the other sides. Substituting h into the first area formula, we obtain the equation for the equilateral triangle area: One leg of that right triangle is equal to height, another leg is half of the side, and the hypotenuse is the equilateral triangle side.Īfter simple transformations, we get a formula for the height of the equilateral triangle: See our right triangle calculator to learn more about right triangles. To find the value of a base (x) in an isosceles triangle, first split the triangle into two congruent right triangles by drawing an altitude. Height of the equilateral triangle is derived by splitting the equilateral triangle into two right triangles. The basic formula for triangle area is side a (base) times the height h, divided by 2: h (a² - (b/2)²) As you can see from the formula above, the altitude of an isosceles triangle is calculated by taking the square root of the difference between the square of the length of one of the sides and the square of half of the length of the base. H = a × √3 / 2, where a is a side of the triangle.īut do you know where the formulas come from? You can find them in at least two ways: deriving from the Pythagorean theorem (discussed in our Pythagorean theorem calculator) or using trigonometry. The formula for a regular triangle area is equal to the squared side times the square root of 3 divided by 4:Īnd the equation for the height of an equilateral triangle looks as follows:
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