Class 8 Maths NCERT Solutions for Chapter – 4 Practical Geometry Ex – 4.1

Practical Geometry

Question 1.
Construct the following quadrilaterals:

(i) Quadrilateral ABCD
AB = 4.5 cm
BC = 5.5 cm
CD = 4 cm
AD = 6 cm
AC = 7 cm

(ii) Quadrilateral JUMP
JU = 3.5 cm
UM = 4 cm
MP = 5 cm
PJ = 4.5 cm
PU 6.5 cm

(iii) Parallelogram MORE
OR = 6 cm
RE = 4.5 cm
EO = 7.5 cm

(iv) Rhombus BEST
BE = 4.5 cm
ET = 6 cm

Solution.

(i)
 First we draw a rough sketch of a quadrilateral ABCD and write down its dimensions as shown.
We may divide it into two conveniently constructible As ABC and ACD.

Steps of Construction :

  • Draw AC = 7 cm.
  • With A as centre and radius 4.5 cm, draw an arc (below AC).
  • With C as centre and radius 5.5 cm, draw another arc cutting the previous arc at B.
  • Join AB and BC.
  • With A as centre and radius 6 cm, draw an arc (above AC).
  • With C as centre and radius 4 cm, draw another arc cutting the previous arc at D.
  • Join AD and CD.
    Then, ABCD is the required quadrilateral.

(ii) First we draw a rough sketch of a quadrilateral JUMP and write down its dimensions as shown.
We may divide it into two conveniently constructible As PJU and PMU.

Steps of Construction :

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry 4

  • Draw PU = 6.5 cm.
  • With P as centre and radius 4.5 cm, draw an arc (below PU).
  • With U as centre and radius 3.5 cm, draw another arc cutting the previous arc at J.
  • Join PJ and JU.
  • With P as centre and radius 5 cm, draw an arc (above PU).
  • With U as centre and radius 4 cm, draw another me cutting the previous arc at M.
  • Join PM and UM.
    Then, JUMP is the required quadrilateral.

(iii) Draw a rough sketch of the’ required parallelogram and write down the given dimensions.

Steps of Construction :

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry 6

  • Draw OR = 6 cm.
  • With O as centre and radius 7.5 cm, draw an arc.
  • With R as centre and radius 4.5 cm, draw another arc to cut the previous arc at E.
  • Join OE and RE.
  • With 0 as centre and radius 4 5 cm 4.5 cm, draw an arc.
  • With E as centre and radius 6 cm, draw another arc to cut the previous arc at M.
  • Join MO and ME.
    Then, MORE is the required parallelogram.

(iv) Draw a rough sketch of the required rhombus and write down the given dimensions.

Steps of Construction :

NCERT Solutions for Class 8 Maths Chapter 4 Practical Geometry 8

  • Draw BE = 4.5 cm.
  • With B as centre and radius 4.5 cm, draw an arc. 4 5 cm
  • With E as centre and radius 6 cm, draw another arc to cut the previous arc at T.
  • Join ST and ET.
  • With T as centre and radius 4.5 cm, draw an arc.
  • With E as centre and radius 4.5 cm, draw another arc to cut the previous arc at S.
  • Join TS and ES.
    Then, BEST is the required rhombus.