NCERT solution Class 9 heron’s formula

NCERT Solutions

Class 9 Maths

Heron’s Formula

NCERT Questions

Ex.12.1 Q.1
Ex.12.1 Q.2
Ex.12.1 Q.3
Ex.13.1 Q.4
Ex.12.1 Q.5
Ex.12.1 Q.6
Ex.12.2 Q.1
Ex.12.2 Q.2
Ex.12.2 Q.3
Ex.12.2 Q.4
Ex.12.2 Q.5
Ex.12.2 Q.5
Ex.12.2 Q.7
Ex.12.2 Q.8
Ex.12.2 Q.9

Ex.12.2 Q.3

Radha made a picture of an aeroplane with coloured paper as shown in the figure.

Find the total area of the paper used.

For the triangle marked I:

a = 5 cm, b = 5 cm, c = 1 cm

s = (a + b + c) = (5 + 5 + 1) ÷ 2 = 11 ÷ 2 = 5.5 cm

Now, Area of the triangle = √ {s (s - a) (s - b) (s - c)}

= √ {5.5(5.5 - 5) (5.5 - 5) (5.5 - 1)}

= √ {5.5 × 0.5 × 0.5 × 4.5}

= √6.1875

= 2.5 cm² (approx.)

For the rectangle marked II:

Length = 6.5 cm, Breadth = 1 cm

Area of the rectangle = 6.5 * 1 cm² = 6.5 cm²

For the trapezium marked III:

Draw AF || DC and AE ⊥ BC

AD = FC = 1 cm, DC = AF = 1 cm

So, BF = BC – FC = (2 – 1) cm = 1 cm

Hence, ∆ABF is equilateral.

Also, E is the mid-point of BF.

Now, BE = 1/2 cm = 0.5 cm

Also, AB² = AE² + BE²

[Pythagoras theorem]

=> AE² = 1² – (0.5)²

=> AE² = 1 – 0.25

=> AE² = 0.75

=> AE = √0.75

⇒ AE = 0.9 cm (approx.)

Area of the trapezium = × (sum of the parallel sides) × (distance between) them.

= × (BC + AD) × AE

= × (2 + 1) × 0.9

= 12 × 3 × 0.9

= 2.7 ÷ 2

= 1.4 cm²

For the triangle marked IV:

It is a right-triangle

∴ Area of the triangle = × base × height

= × 6 × 1.5

= 3 × 1.5

= 4.5 cm²

For the triangle marked V:

This triangle is congruent to the triangle marked IV.

Hence, area of the triangle = 4.5 cm²

Total area of the paper used = (2.5 + 6.5 + 1.4 + 4.5 + 4.5) cm²

= 19.4 cm²

Video solution:

Heron’s Formula Class 9 Maths NCERT Chapter 12 NCERT Solutions

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Attempt to Solve Yourself: Before looking at the solution, try to solve or answer the question independently. This practice will help you test your knowledge and problem-solving skills.
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Refer to Solution Video (if needed): If you encounter difficulty or are unable to solve a question, you can refer to the NCERT solution video on Heron’s Formula Class 9 Maths NCERT Chapter 12 to get a step-by-step explanation of the correct approach. Pay attention to the reasoning and methodology used in the video.
Solve Again Yourself: Once you've understood the solution, attempt to solve the question again by yourself. Repetition and practice solidify your understanding of the concepts and improve retention.
Avoid Memorization: Focus on understanding the underlying principles and concepts behind each solution. Avoid simply memorizing the solutions, as this may hinder your ability to apply the knowledge in different contexts.
Attempt All Questions: Make an effort to attempt all the questions provided in the NCERT textbook. This comprehensive practice will help you cover the entire syllabus and reinforce your understanding across various topics. You may refer Class 9 Maths Heron’s Formula Online Test on LearnoHub.com.
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NCERT solutions of Heron’s Formula Class 9 Maths - all questions of all exercises are solved. Q. No. 1, 2, 3, and so on. Complete explanation and detailed solution makes them the best videos for Class 9 Maths Heron’s Formula NCERT solutions.