An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle
Solution:
Given: Equal sides of the triangle and its perimeter.
Heron's formula for the area of a triangle is: Area = √s(s - a)(s - b)(s - c)
Where a, b, and c are the sides of the triangle, and s = Semi-perimeter = Half the perimeter of the triangle
Equal sides: a = b = 12 cm (given)
The formula for the perimeter of a triangle: Perimeter(P) = a + b + c
30 = 12 + 12 + c (Given, perimeter = 30 cm)
c = 30 - 24
c = 6 cm
Now, Semi Perimeter (s) = P/2 = (a + b + c)/2
s = 30/2
s = 15 cm
By using Heron’s formula,
Area of a triangle = √s(s - a)(s - b)(s - c)
= √15(15 - 12)(15 -12)(15 - 6)
= √15 × 3 × 3 × 9
= √1215
= 9√15 cm2
Area of the triangle = 9√15 cm2
☛ Check: NCERT Solutions Class 9 Maths Chapter 12
Video Solution:
An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle
Class 9 Maths NCERT Solutions Chapter 12 Exercise 12.1 Question 6
Summary:
It is given that there is an isosceles triangle that has a perimeter of 30 cm and each of the equal sides is 12 cm. We have found that its area is 9√15 cm2.
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