An isosceles triangle has perimeter 30 cm and each of the equal sides is 12cm. Find the area of the triangle.?

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its toooo simple lets , start solving........Perimeter triangle= 30 cm12+ 12cm + x = 30 cm x= 6cms= pT/2 = 30/2= 15 cmby using Heron'S formulahope it'll be help U.............

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Given information:
- The perimeter of the isosceles triangle is 30 cm.
- Each of the equal sides of the triangle is 12 cm.

Perimeter of an isosceles triangle:
The perimeter of a triangle is the sum of the lengths of its three sides. In this case, we are given that the perimeter is 30 cm. Since an isosceles triangle has two equal sides, let's denote the length of one of the equal sides as 'a' and the length of the remaining side as 'b'. Therefore, we have:

a + a + b = 30 cm

Since both equal sides are 12 cm, we can substitute 'a' with 12 cm:

12 cm + 12 cm + b = 30 cm

Simplifying the equation, we get:

24 cm + b = 30 cm

Subtracting 24 cm from both sides, we find:

b = 6 cm

Calculating the height:
To find the area of the triangle, we need to calculate its height. In an isosceles triangle, the height is perpendicular to the base and bisects it.

Since the triangle is isosceles, we can draw a line from the vertex angle (opposite the base) to the midpoint of the base. This line is the height of the triangle and creates two congruent right triangles.

Let's denote the height of the triangle as 'h'. Using the Pythagorean theorem, we can find 'h' as follows:

(12 cm / 2)^2 + h^2 = 12 cm^2

Simplifying the equation, we get:

36 cm^2 + h^2 = 144 cm^2

Subtracting 36 cm^2 from both sides, we have:

h^2 = 108 cm^2

Taking the square root of both sides, we find:

h = √108 cm

Simplifying the square root, we get:

h ≈ 10.39 cm

Calculating the area:
Now that we have the height of the triangle, we can calculate its area using the formula:

Area = (base * height) / 2

Substituting the values, we have:

Area = (12 cm * 10.39 cm) / 2

Calculating the area, we find:

Area ≈ 62.34 cm²

Conclusion:
Therefore, the area of the isosceles triangle is approximately 62.34 cm².

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