Therefore, the angles will also be two equal (α) and the other different (β), this being the angle formed by the two equal sides (a).
Two special cases of isosceles triangles are the equilateral triangle and the isosceles right triangle.
And it is obtained that the height h is:
The area of an isosceles triangle is calculated from the base b (the non-repeated side) and the altitude (h) of triangle corresponding to the base. The area is the product of the base and the altitude divided by two, being its formula the following one:
The perimeter of an isosceles triangle is obtained as the addition of the three sides of the triangle. Having two equal sides, the perimeter is twice the repeated side (a) plus the different side (b).
If the repeating side (a) and the angle of the two equal sides are known, the other side (b) should be found by law of cosines.
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Note. Courtesy of the author: José María Pareja Marcano. Chemist. Seville, Spain.
Exercise of the Isosceles Triangle Area
Determine the area of a isosceles triangle knowing its two equal sides (a=3 cm) and the unequal one, whose length is 2 cm (b=2 cm).
What is its area?
Calculate the area using the above formula by multiplying the base by the height:
The isosceles triangle’s area is 2.83 cm2.
Exercise of the Isosceles Triangle Perimeter
Being an isosceles triangle with two equal sides, a=3 cm and a different side of b=2 cm.
What is its perimeter?
To calculate this perimeter we add the repeated side multiplied by two plus the unequal side, i.e.:
It is obtained that the isosceles triangle’s perimeter is 8 cm.
Exercise of the Altitude of an Isosceles Triangle
Find the sides and perimeter of an isosceles triangle whose height referred to the uneven side measures h = 6 cm and the opposite angle, also uneven, 40°.
The side b measures 4.36 cm.
The side a measures 6.38 cm.
Finally, the triangle’s perimeter will measure:
It is obtained that the perimeter of this isosceles triangle will measure 17.12 cm.
AUTHOR: Bernat Requena Serra