Question

1. Construct a quadrilateral ABCD where AB = 5.5 cm, BC = 6,5 cm, CD = 7 cm, ZABC = 120 and
BCD = 90°​

Answer 1

EXERCISE : 4.1

1. Construct the following quadrilaterals:

(i) Quadrilateral ABCD

(ii) Quadrilateral JUMP

AB = 4.5 cm

JU = 3.5 cm

BC = 5.5 cm

UM = 4 cm

AD = 4 cm

MP = 5 cm

AD = 6 cm

PJ = 4.5 cm

AC = 7 cm

PU = 6.5

(iii) Parallelogram MORE

(iv) Rhombus BEST

OR = 6 cm

BE = 4.5 cm

RE = 4.5 cm

ET = 6 cm

EO = 7.5 cm

Sol. (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 Δs ABC and ACD.

Steps of construction:

1. Draw AC = 7 cm.

2. With A as centre and radius 4.5 cm, draw an arc (below AC).

3. With C as centre and radius 5.5 cm, draw another arc cutting the previous arc at B.

4. Join AB and BC

5. With A as centre and radius 6 cm, draw an arc (above AC).

6. With C as centre and radius 4 cm, draw another arc cutting the previous arc and D.

7. Join AD = 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 inot two conveniently constructible Δs PJU and PMU.

Steps of Construction:

1. Draw OR = 5 cm

2. With R as centre and radius equal to 4.5 cm, cut an arc.

3. With O as centre and radius equal to 7.5 cm, cut another arc on the arc drawn in step-2 at point E.

4. With E as centre and radius equal to 6 cm, cut an arc.

5. With O as centre and radius equal to 4.5 cm, cut an arc on the arc drawn in step-4 at point M.

6. Join RE, OE, OM and ME.

Hence, MORE is the required parallelogram.

(iv) We know that all four sides of a rhombus are equal.

∴ BE = ES = ST = BT = 4.5 cm.

Steps of Construction:

1. Draw BE = 4.5 cm.

2. With B as centre and radius equal to 4.5 cm, draw an arc.

3. With E as centre and radius equal to 6 cm, draw another arc, cutting the previous arc at point T.

4. With E as centre and radius equal to 4.5 cm, cut an arc.

5. With T as centre and radius equal to 4.5 cm, cut another arc on the previous arc at point S.

6. Join BT, ES, ET and ST.

Hence, BEST is the required rhombus.

$EXERCISE : 4.1</p><p></p><p>1.  Construct the following quadrilaterals:</p><p></p><p>      (i)   Quadrilateral ABCD</p><p></p><p>      (ii)  Quadrilateral JUMP</p><p></p><p>               AB = 4.5 cm</p><p></p><p>JU = 3.5 cm</p><p></p><p>               BC = 5.5 cm</p><p></p><p>UM = 4 cm</p><p></p><p>               AD = 4 cm</p><p></p><p>MP = 5 cm</p><p></p><p>               AD = 6 cm</p><p></p><p>PJ = 4.5 cm</p><p></p><p>               AC = 7 cm</p><p></p><p>PU = 6.5</p><p></p><p>      (iii) Parallelogram MORE</p><p></p><p>      (iv) Rhombus BEST</p><p></p><p>               OR = 6 cm</p><p></p><p>BE = 4.5 cm</p><p></p><p>               RE = 4.5 cm</p><p></p><p>ET = 6 cm</p><p></p><p>               EO = 7.5 cm</p><p></p><p>Sol.   (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 Δs ABC and ACD.</p><p></p><p>               </p><p></p><p>            Steps of construction:</p><p></p><p>            1.   Draw AC = 7 cm.</p><p></p><p>            2.   With A as centre and radius 4.5 cm, draw an arc (below AC).</p><p></p><p>            3.   With C as centre and radius 5.5 cm, draw another arc cutting the previous arc at B.</p><p></p><p>               </p><p></p><p>            4.   Join AB and BC</p><p></p><p>            5.   With A as centre and radius 6 cm, draw an arc (above AC).</p><p></p><p>            6.   With C as centre and radius 4 cm, draw another arc cutting the previous arc and D.</p><p></p><p>            7.   Join AD = CD.</p><p></p><p>            Then, ABCD is the required quadrilateral.</p><p></p><p>            (ii)  First we draw a rough sketch of a quadrilateral JUMP and write down its dimensions as shown.</p><p></p><p>               </p><p></p><p>            We may divide it inot two conveniently constructible Δs PJU and PMU.</p><p></p><p>               </p><p></p><p>            Steps of construction:</p><p></p><p>            1.   Draw PU = 6.5 cm</p><p></p><p>            2.   With P as centre and radius 4.5 cm, draw an arc(below (PU)</p><p></p><p>               </p><p></p><p>            3.   With U as centre and radius 3.5 cm, draw another arc cutting the previous arc at J.</p><p></p><p>            4.   Join PJ and JU.</p><p></p><p>            5.   With P as centre and radius 5 cm, draw an arc (abov PU).</p><p></p><p>            6.   With U as centre and radius 4 cm, draw another arc cutting the previous arc at M.</p><p></p><p>            7.   Join PM and UM.</p><p></p><p>                  Then, JUMP is the required quadrilateral.</p><p></p><p>            (iii) We know that opposite sides of parallelogram are equal and parallel to each other.</p><p></p><p>                     ∴ OR = ME and MO = ER.</p><p></p><p>            Steps of Construction:</p><p></p><p>            1.   Draw OR = 5 cm</p><p></p><p>            2.   With R as centre and radius equal to 4.5 cm, cut an arc.</p><p></p><p>            3.   With O as centre and radius equal to 7.5 cm, cut another arc on the arc drawn in step-2 at point E.</p><p></p><p>            4.   With E as centre and radius equal to 6 cm, cut an arc.</p><p></p><p>            5.   With O as centre and radius equal to 4.5 cm, cut an arc on the arc drawn in step-4 at point M.</p><p></p><p>            6.   Join RE, OE, OM and ME.</p><p></p><p>                  Hence, MORE is the required parallelogram.</p><p></p><p>               </p><p></p><p>            (iv)  We know that all four sides of a rhombus are equal.</p><p></p><p>                     ∴ BE = ES = ST = BT = 4.5 cm.</p><p></p><p>            Steps of Construction:</p><p></p><p>            1.   Draw BE = 4.5 cm.</p><p></p><p>            2.   With B as centre and radius equal to 4.5 cm, draw an arc.</p><p></p><p>            3.   With E as centre and radius equal to 6 cm, draw another arc, cutting the previous arc at point T.</p><p></p><p>            4.   With E as centre and radius equal to 4.5 cm, cut an arc.</p><p></p><p>               </p><p></p><p>            5.   With T as centre and radius equal to 4.5 cm, cut another arc on the previous arc at point S.</p><p></p><p>            6.   Join BT, ES, ET and ST.</p><p></p><p>                  Hence, BEST is the required rhombus.</p><p></p><p>$

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