Heron S Formula — Class 9 Mathematics NCERT Solutions (Free)

Free step-by-step NCERT solutions for Class 9 Mathematics chapter "Heron S Formula" — 8 important questions with detailed answers for CBSE board exam preparation.

TL;DR: Free step-by-step NCERT solutions for Class 9 Mathematics chapter "Heron S Formula" — 8 important questions with detailed answers for CBSE board exam…

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Key Questions Covered:

  1. State Heron's formula for the area of a triangle: For a triangle with sides a…
  2. Using Heron's formula, find the area of a triangle with sides 10 cm, 10 cm, a…
  3. Find the area of a triangle with sides 13 cm, 14 cm, and 15 cm using Heron's …
  4. + 5 more questions in the full chapter

Solutions Summary:

Question Status
State Heron's formula for the area of a triangle: For a t… ✓ Solved
Using Heron's formula, find the area of a triangle with s… ✓ Solved
Find the area of a triangle with sides 13 cm, 14 cm, and … ✓ Solved

Showing 3 of 8 questions

Q1: State Heron's formula for the area of a triangle: For a triangle with sides a, b, c, the semi-perimeter s = (a+b+c)/2, and area = √[s(s-a)(s-b)(s-c)]. Find the area of a triangle with sides 5 cm, 6 cm, and 7 cm.

Step 1: Heron's Formula: For a triangle with sides a, b, and c: Semi-perimeter s = (a + b + c)/2 Area = √[s(s - a)(s - b)(s - c)] This formula is used when the height is not given but all three sides are known. Step 2: Given sides: a = 5 cm b = 6 cm c = 7 cm Step 3: First, verify that these sides...

Q2: Using Heron's formula, find the area of a triangle with sides 10 cm, 10 cm, and 12 cm (isosceles triangle).

Step 1: Given sides of isosceles triangle: a = 10 cm b = 10 cm c = 12 cm Step 2: Verify triangle inequality: 10 + 10 = 20 > 12 ✓ 10 + 12 = 22 > 10 ✓ 10 + 12 = 22 > 10 ✓ Step 3: Calculate semi-perimeter: s = (a + b + c)/2 s = (10 + 10 + 12)/2 s = 32/2 s = 16 cm Step 4: Calculate the diffe...

Q3: Find the area of a triangle with sides 13 cm, 14 cm, and 15 cm using Heron's formula. Express answer in simplest form.

Step 1: Given sides: a = 13 cm b = 14 cm c = 15 cm Step 2: Verify triangle inequality: 13 + 14 = 27 > 15 ✓ 14 + 15 = 29 > 13 ✓ 13 + 15 = 28 > 14 ✓ Step 3: Calculate semi-perimeter: s = (a + b + c)/2 s = (13 + 14 + 15)/2 s = 42/2 s = 21 cm Step 4: Calculate the differences: s - a = 21 - 1...

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