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Isosceles Triangle Formula

 

An isosceles triangle is a triangle with 2 sides of equal length and 2 equal internal angles adjacent to each equal sides. Unlike an equilateral triangle wherein we can use any vertex to find out the altitude, in an isosceles triangle we are suggested to draw a perpendicular from the vertex which is common to the equal sides.
Let us see how to calculate the area, altitude, and perimeter of an isosceles triangle.
Isosceles Triangle
From figure, let;
a be the measure of the equal sides of an isosceles triangle.
b be the base of the isosceles triangle.
h be the altitude of the isosceles triangle.
The Isosceles Triangle Formulas are,
        Area of an Isosceles Triangle
Perimeter of an Isosceles Triangle
               Altitude of an Isosceles Triangle

Isosceles Triangle Problems

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Some solved problems on isosceles triangle are given below:

Solved Examples

Question 1: Find the area, altitude and perimeter of an isosceles triangle given a = 5 cm ; b = 9 cm?
Solution:

Given,
a = 5 cm
b = 9 cm

Perimeter of an isosceles triangle
= 2a + b
= 2(5) + 9 cm
= 10 + 9 cm
= 19 cm

Altitude of an isosceles triangle
= $\sqrt{a^{2} – \frac{b^{2}}{4}}$

= $\sqrt{5^{2} – \frac{9^{2}}{4}}$ cm

= $\sqrt{25 – \frac{89}{4}}$ cm

= $\sqrt{25-22.25}$ cm

= $\sqrt{2.75}$ cm

= 1.658 cm

Area of an isosceles triangle
= $\frac{b\times h}{2}$

= $\frac{9\times 1.658}{2}$ cm²

= $\frac{14.92}{2}$ cm²

= 7.461 cm²

Question 2: Find the area, altitude and perimeter of an isosceles triangle given a = 12 cm ; b = 7 cm ?
Solution:

Given,
a = 12 cm
b = 7 cm

Perimeter of an isosceles triangle
= 2a + b
= 2(12) + 7 cm
= 24 + 7 cm
= 31 cm

Altitude of an isosceles triangle
= $\sqrt{a^{2}-\frac{b^{2}}{4}}$

= $\sqrt{12^{2}-\frac{7^{2}}{4}}$ cm

= $\sqrt{144-\frac{49}{4}}$ cm

= $\sqrt{144-12.25}$ cm

= $\sqrt{131.75}$ cm

= 11.478 cm

Area of an isosceles triangle
= $\frac{b\times h}{2}$

= $\frac{7\times 11.478}{2}$ cm²

= $\frac{80.346}{2}$ cm²

= 40.173 cm²

For more: Math Formulas.

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