![]() ![]() This article has been viewed 686,467 times. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. How to Find the Area of an Isosceles Triangle The area of an isosceles triangle can be derived by using Herons formula : Area (A) b/4(4a 2 - b 2 ), where a is the length of the equal side and b is the base of the triangle. There are 9 references cited in this article, which can be found at the bottom of the page. In a right isosceles triangle, the equal sides join to form the right angle and the hypotenuse is the unequal side. The angle opposite the base is called the vertex angle, and the point. ![]() In an isosceles triangle, the two equal sides are called legs, and the remaining side is called the base. Isosceles triangles are very helpful in determining unknown angles. If all three side lengths are equal, the triangle is also equilateral. Additionally, David has worked as an instructor for online videos for textbook companies such as Larson Texts, Big Ideas Learning, and Big Ideas Math. An isosceles triangle is a triangle that has (at least) two equal side lengths. ![]() After attaining a perfect 800 math score and a 690 English score on the SAT, David was awarded the Dickinson Scholarship from the University of Miami, where he graduated with a Bachelor’s degree in Business Administration. With over 10 years of teaching experience, David works with students of all ages and grades in various subjects, as well as college admissions counseling and test preparation for the SAT, ACT, ISEE, and more. David Jia is an Academic Tutor and the Founder of LA Math Tutoring, a private tutoring company based in Los Angeles, California. "Isosceles Triangle.This article was co-authored by David Jia. a and b are known find c, P, s, K, ha, hb, and hcįor more information on right triangles see:.Given sides a and b find side c and the perimeter, semiperimeter, area and altitudes Altitude c of Isosceles Triangle: hc = (b/2a) * √(4a 2 - b 2). ![]() Altitude b of Isosceles Triangle: hb = (1/2) * √(4a 2 - b 2).Altitude a of Isosceles Triangle: ha = (b/2a) * √(4a 2 - b 2).Area of Isosceles Triangle: K = (b/4) * √(4a 2 - b 2).A right triangle can be scalene (having all three sides of different length) or isosceles (having exactly two sides of equal length). Semiperimeter of Isosceles Triangle: s = (a + b + c) / 2 = a + (b/2) The two perpendicular sides are called the legs of a right triangle, and the longest side that lies opposite the 90-degree is called the hypotenuse of a right triangle.Perimeter of Isosceles Triangle: P = a + b + c = 2a + b.To find the ratio number of the hypotenuse h, we have, according to the Pythagorean theorem, h2 1 2 + 1 2 2. In an isosceles right triangle, the equal sides make the right angle. Altitudes of Isosceles Triangle: ha = hc In an isosceles right triangle the sides are in the ratio 1:1.It follows that any triangle in which the sides satisfy this condition is a right triangle. Let us know if you have any other suggestions! Formulas and Calculations for an isosceles triangle: Now consider the isosceles right triangle with the two equal sides being 1 unit. A right isosceles triangle is an isosceles triangle with a vertex angle equal to 90°. For any right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the two other sides. Once we know sides a, b, and c we can calculate the perimeter = P, the semiperimeter = s, the area = K, and the altitudes: For example, if we know a and b we know c since c = a. In our calculations for a right triangle we only consider 2 known sides to calculate the other 7 unknowns. Triangle where 2 sides, a and c, are equal and 2 angles, A and C, are equal. Calculator UseĪn isosceles triangle is a special case of a In general, when it comes to a triangle, we have a nice formula that we can use to find its area. *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 triangle with two sides of equal length, like the one shown here. ![]()
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