Using two angles and length between them: A =.Using the length of 2 sides and an angle between them: Area = ½ × b × a × sin(α).Using base and Height: Area = ½ × b × h.The area of an isosceles triangle can be calculated in many ways based on the known elements of the isosceles triangle. The area of an isosceles triangle refers to the total space covered by the shape in 2-D. What is the Formula for Area of Isosceles Triangle? The perpendicular from the vertex angle bisects the base and it also bisects the vertex angle.The side opposite the vertex angle is called the base and base angles are equal.The two equal sides of an isosceles triangle are called the legs and the angle between them is called the vertex angle or apex angle.Here are some properties of an Isosceles triangle that distinguish it from other types of triangles:

What is an Isosceles Triangle?Īn isosceles triangle is defined as a triangle having two sides equal, which also means two equal angles. Thus, the area of an isosceles triangle means the total space enclosed by an isosceles triangle. The area of a figure is the region enclosed by the figure. ⇒ Area = (a + b/2 − a) × √Īrea of isosceles triangle = b/2 × √(a 2 − b 2/4) square unitsįAQs on Area of an Isosceles Triangle What Does the Area of an Isosceles Triangle Mean? Here, s is half of the perimeter of the triangle, and hence, it is called semi-perimeter. We know that the perimeter of a triangle with sides a, b, and c is a + b + c. s is the semi perimeter of the triangle.a, b, and c are the sides of the triangle.The Heron's formula to find the area, A of a triangle whose sides are a,b, and c is: Heron's formula is used to find the area of a triangle when the measurements of its 3 sides are given. The area of an isosceles triangle formula can be easily derived using Heron’s formula as explained in the following steps. β = measure of the angle opposite to the base.α = measure of equal angles of the isosceles triangle.a = measure of equal sides of the isosceles triangle.Length of 2 sides and an angle between them.Known Parameters of Given Isosceles Triangleįormula to Calculate Area (in square units) The following table summarizes different formulas that can be used to calculate the area of an isosceles triangle, for a different set of known parameters. The general basic formula that can be used to calculate the area of an isosceles triangle using height is given as, (1/2) × Base × Height Isosceles Triangle Area Using Trigonometry(SAS and ASA) Isosceles Triangle Area Using Heron’s Formula Let us understand the area of the isosceles triangle in detail in the following section. Scalene Triangle- A triangle with all unequal sides.Isosceles Triangle- A triangle with any two sides/angles equal.Equilateral Triangle- A triangle with all sides equal.These different types based on sides are given below: Besides the general area of the isosceles triangle formula, which is equal to half the product of the base and height of the triangle, different formulas are used to calculate the area of triangles, depending upon their classification based on 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 area of an isosceles triangle is the amount of space enclosed between the sides of the triangle.

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. 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 = 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:

Isosceles right triangle area