Third side is 32 – (8 + 11) = 13 cm. Semi-perimeter s = 32 / 2 = 16 cm. By Heron’s formula, area = √(16 x (16 – 8) x (16 – 11) x (16 – 13)) = √(16 x 8 x 5 x 3) = 8√30 cm² (approx 43.82 cm²).
Find the area of a triangle, given that its sides are 8 cm and 11 cm long, and its perimeter is 32 cm.
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Given perimeter = 32 cm and two sides a = 8 cm, b = 11 cm.
Third side c = 32 – (8 + 11) = 32 – 19 = 13 cm.
Semi-perimeter s = perimeter / 2 = 32 / 2 = 16 cm.
Now apply Heron’s formula:
Area = √(s x (s – a) x (s – b) x (s – c))
Area = √(16 x (16 – 8) x (16 – 11) x (16 – 13))
Area = √(16 x 8 x 5 x 3)
Area = √(16 x 4 x 2 x 15)
Area = 4 x 2 x √30 = 8√30 cm² (approximately 43.82 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/