Way 1: Since 7² + 24² = 49 + 576 = 625 = 25², it is a right triangle, so Area = (1/2) x 7 x 24 = 84 cm². Way 2: Semi-perimeter s = 28 cm; Heron’s formula yields √(28 x 21 x 4 x 3) = 84 cm².
The sides of a triangle have lengths 7 cm, 24 cm, 25 cm. Find the area of the triangle in two different ways.
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Method 1 (Right Triangle Formula):
Check sides with Pythagoras theorem: 7² + 24² = 49 + 576 = 625 = 25².
This is a right-angled triangle with base 7 cm and height 24 cm.
Area = (1/2) x base x height = (1/2) x 7 x 24 = 84 cm².
Method 2 (Heron’s Formula):
Semi-perimeter s = (7 + 24 + 25) / 2 = 56 / 2 = 28 cm.
Area = √(28 x (28 – 7) x (28 – 24) x (28 – 25))
= √(28 x 21 x 4 x 3)
= √(7056) = 84 cm².
Both methods give 84 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/