The base is 40 – (15 + 15) = 10 cm. Semi-perimeter s = 20 cm. By Heron’s formula, area = √(20 x (20 – 15) x (20 – 15) x (20 – 10)) = √(20 x 5 x 5 x 10) = 50√2 cm² (approx 70.71 cm²).
An isosceles triangle has perimeter 40 cm; the equal sides are 15 cm each. Find the area of the triangle.
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Given equal sides a = 15 cm, b = 15 cm and perimeter = 40 cm.
Third side (base) c = 40 – (15 + 15) = 40 – 30 = 10 cm.
Semi-perimeter s = 40 / 2 = 20 cm.
Using Heron’s formula:
Area = √(s x (s – a) x (s – b) x (s – c))
Area = √(20 x (20 – 15) x (20 – 15) x (20 – 10))
Area = √(20 x 5 x 5 x 10)
Area = √(5000) = √(2500 x 2) = 50√2 cm².
In decimal form, 50 x 1.414 is approximately 70.71 cm².
Hence, the area of the triangle is 50√2 cm² (or 70.71 cm²).
For more NCERT Solutions of Class 9 Ganita Manjari Chapter 6 Measuring Space: Perimeter and Area Question Answer (2026-27)
https://www.tiwariacademy.com/ncert-solutions/class-9/maths/ganita-manjari-chapter-6/