# 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

**Solution:**

- Based on the given information, the five given measurements are of 4 sides and one diagonal. When measurements of 4 sides and one diagonal of a quadrilateral is given, we can construct a quadrilateral (Page 58 of Grade 8 NCERT Book)
- All sides of a rhombus are equal and opposite sides are parallel, measurements of all sides can be found.

(i) Quadrilateral ABCD

Let us first draw a rough sketch of quadrilateral.

The construction can be done in two parts. First draw ∆LIF and then daw ∆LTF and then join the other side. Let us see whether it is possible

In ∆LIF,

4 + 3 > 4.5 and 4 - 3 < 4.5

4.5 + 3 > 4 and 4.5 - 3 < 4

4.5 + 4 > 3 and 4.5 - 4 < 3

In ∆LTF,

4 + 4 > 2.5 and 4 - 4 < 2.5

4 + 2.5 > 4 and 4 - 2.5 < 4

4 + 2.5 > 4 and 4 - 2.5 < 4

In both cases, it is possible to form triangle.

Let us construct the quadrilateral.

Step 1: Construct Line LI=4 cm. With L as center and 4.5 cm as radius draw an arc. With I as center and 3 cm as radius draw an arc cutting the former one. The intersection point is F. Join IF and LF.

Step 2: With L as center and radius 2.5 cm draw an arc. With I as center and 4 cm as radius draw an arc cutting the former one at T. Join LT and IT.

Step 3: Join FT.

Step 4: LIFT is the required quadrilateral.

(ii) Quadrilateral GOLD

Step 1: Draw a line segment OL = 7.5 cm

Step 2: With O as centre and radius 10 cm draw an arc.

Step 3: With L as centre and radius 5cm draw another arc to meet the former arc at D.

Step 4: Join OD and LD.

Step 5: With L and D as centre and equal radii 6 cm draw an arc to meet each other at G.

Step 6: Join LG and DG.

GOLD is the required quadrilateral.

(iii) Rhombus BEND

BN = 5.6 cm

DE = 6.5 cm

All sides of a rhombus are equal and opposite sides are parallel, measurements of all sides can be found.

Step 1: Draw a line segment BN = 5.6 cm.

Step 2: Draw the perpendicular bisector of BN intersecting at O.

Step 3: Draw two arcs with centre O and radius 3.25 cm to meet the right bisector at D and E.

Step 4: Join BE, EN, ND and BD.

Thus, BEND is the required rhombus.

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

**Video Solution:**

## 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

NCERT Solutions for Class 8 Maths Chapter 4 Exercise 4.2 Question 1

**Summary:**

The following quadrilaterals are constructed (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

**☛ 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 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
- 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?