# 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:**

i) Step 1: Draw a line segment MO= 6 cm.

Step 2: With M as center draw angle of measure 60^{o}*.*

Step 3: Draw 105º from O.

Step 4: With O as center and radius 4.5 cm draw an arc cutting the ray from O at R. OR = 4.5 cm

Step 5: Construct an angle of 105º from R as above. The ray from R meets the ray from M at a point. Mark the intersection point as E.

Step 6: MORE is the required quadrilateral.

ii) Step 1: Draw a line segment LA = 6.5 cm

Step 2: Draw an angle of 75° at point L and 110° at point A with the help of a protractor.

[∵ 360° – (110° + 90° + 85°) = 75°]

Step 3: Cut LP = 4 cm.

Step 4: Draw an angle of 90° at point P which meets the angle line through point A at point N.

Thus PLAN is the required quadrilateral.

iii) Opposite sides of a parallelogram are equal.

Step 1: Draw a line segment HE = 5 cm.

Step 2: Draw an angle of 85° at E and cut EA = 6 cm.

Step 3: With centre A and radius 5 cm draw an arc.

Step 4: Draw another arc with centre H and radius 6 cm to meet the former arc at R.

Step 5: Join the points HR and AR.

HEAR is the required parallelogram.

iv) All the angles of the rectangle are of 90°.

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

Step 2: Draw the angle of 90° at point K and cut KA = 5 cm.

Step 3: With centre O and radius 5 cm draw an arc.

Step 4: Draw another arc with centre A and radius 7 cm to meet the former arc at Y.

Step 5: Join points OY and AY.

OKAY is the required rectangle.

**☛ Check: **NCERT Solutions for Class 8 Maths Chapter 4

**Video Solution:**

## 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

NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.3 Question 1

**Summary:**

The following quadrilaterals are constructed (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

**☛ Related Questions:**

- 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 and ET = 6 cm.
- Construct the following quadrilaterals. (i) Quadrilateral LIFT LI = 4 cm, IF = 3 cm TL = 2.5 cm, LF = 4.5 cm, IT = 4 cm (ii) Quadrilateral GOLD OL = 7.5 cm, GL = 6 cm GD = 6 cm, LD = 5 cm, OD = 10 cm (iii) Rhombus BEND BN = 5.6 cm and DE = 6.5 cm.
- Construct the following quadrilaterals. (i) Quadrilateral DEAR DE = 4cm, EA = 5cm, AR = 4.5cm ∠E = 60°, ∠A = 90° (ii) Quadrilateral TRUE TR = 3.5cm, RU = 3cm, UE = 4cm ∠R = 75°, ∠U = 120°
- Draw the following. 1. A square READ with RE = 1 cm. 2. A rhombus whose diagonals are 5.2 cm and 6.4 cm long. 3. A rectangle with adjacent sides of lengths 5 cm and 4 cm 4. A parallelogram OKAY where OK = 5.5 cm and KA = 4.2 cm. Is it unique?

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