NCERT Solutions for Class 8 Maths Chapter 4 - Practical Geometry Exercise 4.2

The NCERT Solutions for Class 8 Maths include topics with engaging math challenges and activities that strengthen math concepts. Each question of the exercise in NCERT Class 8 Maths Solutions has been carefully solved for the students to understand, keeping the examination point of view in mind.

Class 8 Maths Chapter 4 – Practical Geometry Exercise 4.2 Questions and answers help the students to understand the construction of a quadrilateral when two diagonals and three sides are given. These NCERT Solutions are prepared by BYJU’S subject experts using a step-by-step approach.

NCERT Solutions for Class 8 Maths Chapter 4 – Practical Geometry Exercise 4.2

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Access Other Exercise Solutions of Class 8 Maths Chapter 4 – Practical Geometry

Exercise 4.1 Solutions 1 Question

Exercise 4.3 Solutions 1 Question

Exercise 4.4 Solutions 1 Question

Exercise 4.5 Solutions 4 Questions

Access Answers to NCERT Class 8 Maths Chapter 4 – Practical Geometry Exercise 4.2 Page Number 62

1. Construct the following quadrilaterals.

(i) Quadrilateral LIFT LI = 4 cm

IF = 3 cm TL = 2.5 cm LF = 4.5 cm

IT = 4 cm

Solution:

A rough sketch of the quadrilateral LIFT can be drawn as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 17

(1) ∆ ITL can be constructed by using the given measurements as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 18

(2) Vertex F is 4.5 cm away from vertex L and 3 cm away from vertex I. ∴, while taking L and I as centres, draw arcs of 4.5 cm radius and 3 cm radius, respectively, which will be intersecting each other at point F.

NCERT Solution For Class 8 Maths Chapter 4 Image 19

NCERT Solution For Class 8 Maths Chapter 4 Image 20

(3) Join F to T and F to I.

LIFT is the required quadrilateral.

(ii) Quadrilateral GOLD OL = 7.5 cm

GL = 6 cm GD = 6 cm LD = 5 cm OD = 10 cm

Solution:

The rough sketch of the quadrilateral GOLD can be drawn as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 21

(1) ∆ GDL can be constructed by using the given measurements as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 22

(2) Vertex O is 10 cm away from vertex D and 7.5 cm away from vertex L. Therefore, while taking D and L as centres, draw arcs of 10 cm radius and 7.5 cm radius, respectively. These will intersect each other at point O.

NCERT Solution For Class 8 Maths Chapter 4 Image 23

(3) Join O to G and L.

NCERT Solution For Class 8 Maths Chapter 4 Image 24

GOLD is the required quadrilateral.

(iii) Rhombus BEND

BN = 5.6 cm

DE = 6.5 cm

Solution:

We know that the diagonals of a rhombus always bisect each other at 90º.

Let us assume that these intersect at point O in this rhombus. Hence, EO = OD = 3.25 cm

The rough sketch of the rhombus BEND can be drawn as follows.

NCERT Solution For Class 8 Maths Chapter 4 Image 25

(1) Draw a line segment BN of 5.6 cm and also draw its perpendicular bisector. Let it intersect the line segment BN at point O.

NCERT Solution For Class 8 Maths Chapter 4 Image 26

(2) Taking O as the centre, draw arcs of 3.25 cm radius to intersect the perpendicular bisector at points D and E.

NCERT Solution For Class 8 Maths Chapter 4 Image 27

(3) Join points D and E to points B and N.

NCERT Solution For Class 8 Maths Chapter 4 Image 28

BEND is the required quadrilateral.


Exercise 4.2 of NCERT Solutions for Class 8 Maths Chapter 4- Practical Geometry is based on the following topic:

  1. Constructing a Quadrilateral
    • When two diagonals and three sides are given

Also, explore – 

NCERT Solutions for Class 8

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