Skip to content
Related Articles

Related Articles

Class 8 NCERT Solutions – Chapter 4 Practical Geometry – Exercise 4.3
  • Last Updated : 04 Jan, 2021
GeeksforGeeks - Summer Carnival Banner

Construct the following quadrilaterals:

  1. Quadrilateral MORE
    MO = 6 cm, ∠R = 105°, OR = 4.5 cm, ∠M = 60°, ∠O = 105°
     
  2. Quadrilateral PLAN
    PL = 4 cm, LA = 6.5 cm, ∠P = 90°, ∠A = 110°, ∠N = 85°
     
  3. Parallelogram HEAR
    HE = 5 cm, EA = 6 cm, ∠R = 85°
     
  4. Rectangle OKAY
    OK = 7 cm, KA = 5 cm

Solutions:

1. Quadrilateral MORE

Given

MO = 6 cm, ∠R = 105°, OR = 4.5 cm, ∠M = 60°, ∠O = 105°

Steps for Construction

Step 1: Draw a line ‘OR’ measuring = 4.5 cm.

Step 2: Draw angles of 105° from both the points ‘O’ and ‘R’, as shown below

Step 3: Open an arc of 6 cm then cut ‘OM’ of 6 cm, as shown in the figure below
 



Step 4: Now make an angle of 60° from point ‘M’ which will further join point ‘E’.

Step 5: We have the quadrilateral ‘MORE’
 

2. Quadrilateral PLAN

Given

PL = 4 cm, LA = 6.5 cm, ∠P = 90°, ∠A = 110°, ∠N = 85°

First we will find angle L,
Sum of angles of a quadrilateral = 360°
∠P + ∠A + ∠N + ∠L = 360°
90° + 110° + 85° + ∠L = 360°
∠L = 360° – 285°
∠L = 75°

Steps for Construction

Step 1: Draw a line segment LA = 6.5 cm.

Step 2: Draw an angle of 75° from point L.



Step 3: Draw another angle of 110° from point A

Step 4: From point L cut PL=4 cm.

Step 5: From point P draw an angle of 90° which intersect the angle line extended through A at N.
 

Hence, we have our required quadrilateral PLAN.

3. Parallelogram HEAR

Given

HE = 5 cm, EA = 6 cm, ∠R = 85°

Steps for Construction

Step 1: Draw a line segment HE = 5 cm

Step 2: From point E draw an angle of 85°.

Step 3: From point E cut EA = 6 cm

Step 4: Draw an arc from center A of 5 cm, draw another arc of 6 cm with center E, and further mark point R at the intersection of both the arcs. as shown below:

Step 5: Join HR and AR respectively.
 

Thus, we have the required quadrilateral HEAR.

4. Rectangle OKAY

Given

OK = 7 cm, KA = 5 cm

All the angles of a rectangle are 90° and the opposite sides are equal.

Steps for Construction

Step 1: Draw a line segment OK = 7 cm.

Step 2: Draw an 90° angle from point O.

Step 3: Taking point O as radius draw an arc of 5 cm as shown, and mark the point Y.

Step 4: Taking Points K and Y as centre draw arcs of 5 cm and 7 cm respectively, intersect both the arcs at point A.
 

Step 5: Join KA and AY.
 

Thus, we have the required rectangle OKAY.

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.

My Personal Notes arrow_drop_up
Recommended Articles
Page :