• Skip to main content
  • Skip to primary sidebar
  • Skip to footer
  • NCERT Solutions
    • NCERT Books Free Download
  • TS Grewal
    • TS Grewal Class 12 Accountancy Solutions
    • TS Grewal Class 11 Accountancy Solutions
  • CBSE Sample Papers
  • NCERT Exemplar Problems
  • English Grammar
    • Wordfeud Cheat
  • MCQ Questions

CBSE Tuts

CBSE Maths notes, CBSE physics notes, CBSE chemistry notes

NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2

NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.

  • Heron’s Formula Class 9 Ex 12.1
  • Heron’s Formula Class 9 Ex 12.2
Board CBSE
Textbook NCERT
Class Class 9
Subject Maths
Chapter Chapter 12
Chapter Name Heron’s Formula
Exercise  Ex 12.2
Number of Questions Solved 9
Category NCERT Solutions

NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2

Ex 12.2 Class 9 Maths Question 1.
A park in the shape of a quadrilateral ABCD has ∠C = 90°, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?
Solution:
Given, quadrilateral ABCD in which AB = 9 m, BC = 12 m, CD = 5 m, AD = 8 m and ∠C = 90°. Now, join the diagonal BD which divides quadrilateral ABCD into two triangles.
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.1
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.2

Ex 12.2 Class 9 Maths Question 2.
Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD 4 cm, DA = 5 cm and
AC = 5 cm.
Solution:
Area of quadrilateral ABCD = Area of Δ ABC + Area of Δ ACD
In Δ ABC,
We have, AB = 3 cm, BC = 4 cm, CA = 5 cm
Therefore, AB2 + BC2 = 32 + 42 = 9 +16 = 25 = (5)2 = CA2
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.3

Ex 12.2 Class 9 Maths Question 3.
Radha made a picture of an aeroplane with coloured paper as shown in figure. Find the total area of the paper used.
Solution:
For region I (triangle),
Let a = 5 cm, b = 5 cm and c = 1 cm
Then, semi-perimeter of I triangle
\( s=\cfrac { a+b+c }{ 2 } =\cfrac { 5+5+1 }{ 2 } =\cfrac { 11 }{ 2 } cm \)
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.4
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.5
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.6
Similarly area of region IV (right angled triangle )
= 4.5 cm2 [Since, it has same dimensions as region V]
∴ Total area of paper used = Area of region I + Area of region II + Area of region III +Area of region IV + Area of region V
= 2.49 + 6.5 +1. 30 + 4.5 + 4.5= 19.29 = 19.3 cm2 (approx.)

Ex 12.2 Class 9 Maths Question 4.
A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
Solution:
Let ABC be a triangle with sides
AB = 26 cm, BC = 28 cm, CA = 30 cm
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.7
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.8

Ex 12.2 Class 9 Maths Question 5.
A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
Solution:
Given, ABCD is a rhombus shaped field whose each side is 30 m and longer diagonal AC is 48 m.
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.9
Clearly, the diagonal AC divides the rhombus into two triangles, Δ ABC and Δ ADC which are congruent.
Area of Δ ABC = Area of Δ ADC
Also, Δ ABC and Δ ADC have equal perimeters.
Now, semi-perimeter of Δ ABC,
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.10
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.11

Ex 12.2 Class 9 Maths Question 6.
An umbrella is made by stitching 10 triangular pieces of cloth of two different colors, each piece measuring 20 cm, 50 cm, and 50 cm. How much cloth of each color is required for the umbrella?
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.12
Solution:
Let given sides of one triangular piece of cloth be a = 20 cm, b = 50 cm and c = 50 cm.
Then, semi-perimeter of one triangular piece.
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.13

Ex 12.2 Class 9 Maths Question 7.
A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm, each is to be made of three different shades as shown in the figure. How much paper of each shade has been used in it?
Solution:
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.14
Let the kite is made square ABCD and an isosceles ADEF.
Given, sides of ADEF are DE = DF = 6 cm and EF = 8 cm.
Also, diagonal of square ABCD = 32 cm
We know that diagonals of a square bisect each other at right angle.
OA = OB = OC = OD = \(\cfrac { 32 }{ 2 } \) = 16 cm
Now, area of region I = 2 x Area of AAOB = 2 x \(\cfrac { 1 }{ 2 } \) x OA x OB
[∵ area of right angled triangle = \(\cfrac { 1 }{ 2 } \) x base x height]
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.15
Hence, the area of paper of I color used in making kite = 256 cm2 Area of paper of II color used in making kite = 256 cm2 and area of paper of III color used in making kite = 17.92 cm2

Ex 12.2 Class 9 Maths Question 8.
A floral design on a floor is made up of 16 tiles, which are triangular, the sides of the triangle being 28 cm, 9 cm and 35 cm, Find the cost of polishing the tiles at the rate of 50 paise per cm2.
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.16
Solution:
Given, length of the side of the triangular tile are 28 cm, 9 cm, and 35 cm.
Let a = 28 cm, b = 9 cm and c = 35 cm
Then, semi-perimeter of one triangular tile,
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.17

Ex 12.2 Class 9 Maths Question 9.
A field is in the shape of a trapezium, whose parallel sides are 25 m and 10 m and the non-parallel sides are 14 m and 13 m. Find the area of the field.
Solution:
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.18
Let ABCD be the given field in the form of a trapezium in which AB = 25 m and CD = 10 m, BC = 13 m, AD = 14 m and DC || AB.
Through C, draw CE||DA and let it meets AB at E.
Let CP h m be the height of the trapezium.
Now, DC || AE     [∵ DC 11 AB given]
and  CE||DA       [by construction]
Thus, AECD is a parallelogram.
⇒ AE = DC = 10 m and CE = DA = 14 m
In A CEB, we have, CB = 13m, CE = 14 m
and BE = AB – AE = 25 -10 = 15 m
Let a = 14 m, b = 13 m and c = 15 m
NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2.19

We hope the NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula Ex 12.2 help you. If you have any query regarding NCERT Solutions for Class 9 Maths Chapter 12 Heron’s Formula EX 12.2, drop a comment below and we will get back to you at the earliest.

Primary Sidebar

NCERT Exemplar problems With Solutions CBSE Previous Year Questions with Solutoins CBSE Sample Papers

Recent Posts

  • Letter to The Editor Class 12 CBSE Format, Samples and Examples
  • Speech Writing Format CBSE Class 11 Examples, Samples, Topics
  • Report Writing Class 12 Format, Examples, Topics, Samples
  • Decimals
  • CBSE Class 12 English Letter Writing – Letters Of Application for Jobs
  • NCERT Exemplar Problems Class 7 Maths – Exponents and Powers
  • NCERT Exemplar Class 7 Maths Practical Geometry Symmetry and Visualising Solid Shapes
  • NCERT Exemplar Class 7 Maths Algebraic Expression
  • NCERT Solutions for Class 11 Maths Chapter 8 Binomial Theorem Ex 8.2
  • NCERT Exemplar Problems Class 7 Maths – Perimeter and Area
  • NEET Physics Chapter Wise Mock Test – General properties of matter
  • ML Aggarwal Class 10 Solutions for ICSE Maths Chapter 6 Factorization MCQS
  • Division of a Polynomial by a Monomial
  • Multiplication-Decimal Numbers
  • Proper, Improper and Mixed fractions

Footer

Maths NCERT Solutions

NCERT Solutions for Class 12 Maths
NCERT Solutions for Class 11 Maths
NCERT Solutions for Class 10 Maths
NCERT Solutions for Class 9 Maths
NCERT Solutions for Class 8 Maths
NCERT Solutions for Class 7 Maths
NCERT Solutions for Class 6 Maths

SCIENCE NCERT SOLUTIONS

NCERT Solutions for Class 12 Physics
NCERT Solutions for Class 12 Chemistry
NCERT Solutions for Class 11 Physics
NCERT Solutions for Class 11 Chemistry
NCERT Solutions for Class 10 Science
NCERT Solutions for Class 9 Science
NCERT Solutions for Class 7 Science
MCQ Questions NCERT Solutions
CBSE Sample Papers
cbse ncert
NCERT Exemplar Solutions LCM and GCF Calculator
TS Grewal Accountancy Class 12 Solutions
TS Grewal Accountancy Class 11 Solutions