An isosceles triangle has side lengths of 7 cm, 7 cm, and 10 cm. Therefore, the area of the isosceles triangle is 24 square cm.Įxample 3. Given an isosceles triangle with a base of length 8 cm and a height of 6 cm. Let us say that they both measure x then, Area 1 2 × x × x. Since in an isosceles right triangle, base and perpendicular are of equal length. We know that area of an isosceles triangle 1 2 × base × perpendicular. The angle 14.5° and leg b 2.586 ft are displayed as well. Each right triangle has an angle of ½, or in this case (½) (120) 60 degrees. It should be noted that an isosceles triangle is a triangle with two congruent sides and so, the altitude bisects the base and vertex. ![]() The isosceles triangle altitude bisects the angle of the vertex and bisects the base. Draw a line down from the vertex between the two equal sides, that hits the base at a right angle. Hence, is the altitude of a right triangle. Ladder length, our right triangle hypotenuse, appears Its equal to 10.33 ft. Divide the isosceles into two right triangles. Therefore, the area of the isosceles triangle is 10 square inches.Įxample 2. Step 1: Find the length of the base: Given that the area of an isosceles right triangle is 8 cm 2. Enter the given values.Our leg a is 10 ft long, and the angle between the ladder and the ground equals 75.5°. Using the formula for the area of an isosceles triangle: In an isosceles triangle, the lengths of the two equal sides are both 5 inches, and the height is 4 inches. Solved Examples on the Area of Isosceles TriangleĮxample 1. ![]() It is important to note that the area of an isosceles triangle is always non-negative and is expressed in square units, such as square centimetres (cm²) or square inches (in²). Substituting the lengths of an isosceles triangle, we get, Since the legs are equal AB BC, then we obtain:: We can rewrite this formula: The property is proved. Where, s is the semi perimeter of the triangle and a, b and c are lengths of sides of a triangle. Heron’s formula is a general formula for calculating the area of any triangle using the lengths of its sides. If the lengths of all three sides of the isosceles triangle are known, Heron’s formula can be used to calculate the area. It is important to ensure that the height is measured perpendicularly to the base for accurate calculations. ![]() In this formula, the base and height are multiplied by half to obtain the area.
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