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Question:

Construct the following quadrilaterals:
(i) Quadrilateral MORE: MO = 6 cm, OR = 4.5 cm, ∠M = 60°, ∠O = 105°, ∠R = 105°
(ii) Quadrilateral PLAN: PL = 4 cm, LA = 6.5 cm, ∠P = 90°, ∠A = 110°, ∠N = 85°
(iii) Parallelogram HEAR: HE = 5 cm, EA = 6 cm, ∠R = 85°
(iv) Rectangle OKAY: OK = 7 cm, KA = 5 cm

Solution:

    1. Draw MO of length 6cm.
  1. Draw an angle of 105 degrees on O and cut an arc of 4.5cm on it. The point of intersection is R.
  2. Draw an angle of 105 degrees on R and draw an angle of 60 degrees on M. Their point of intersection is E.
  3. Join all the points. MORE is the required quadrilateral.
    1. Draw PL of length 4cm.
  1. Calculate the value of ∠L, which comes out to be 75°. Draw an angle of 75° on L and cut an arc of 6.5cm on it. The point of intersection is A.
  2. Draw an angle of 110° on A and draw an angle of 90° on P. Their point of intersection is N.
  3. Join all the points. PLAN is the required quadrilateral.
    1. Draw EA of length 6cm.
  1. Draw an angle of 85° on E and cut an arc of 5cm on it. The point of intersection is H. (∠R = ∠E = 85° and ∠H = 95°)
  2. Draw an angle of 95° on H and cut an arc of 6cm. Their point of intersection is R.
  3. Join all the points. HEAR is the required parallelogram.
    1. Draw OK of length 7cm.
  1. Draw an angle of 90° on K and cut an arc of 5cm on it. The point of intersection is A.
  2. Draw an angle of 90° on A and cut an arc of 7cm from A. The point of intersection is Y.
  3. Join all the points. OKAY is the required rectangle.