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Question 1

Construct a quadrilateral ABCD in which AB = 4.5 cm, BC = 4cm, CD = 6.5 cm, DA = 3cm and BD = 6.5 cm.

Solution:

Steps of construction:

1. Draw BD = 6.5cm.
2. With B as centre and BC (=4cm) as radius draw an arc.
3. With D as centre and DC (=6.5cm) as radius draw another arc to cut the arc of step 2 at C.
4. With B as centre and BA (=4.5cm) draw an arc.
5. With D as centre and DA (=3cm) draw another arc to cut the arc of step 4 as A.
6. Join BC, CD, AB and AD.

Then, ABCD is the required quadrilateral.

 

Question 2

Construct a rhombus with side 4.5 cm and one diagonal 6 cm.


Solution:




Steps of construction:

1. Draw AC = 6 cm.
2. With A as centre and 4.5cm as radius draw two arcs on either side of AC.
3. With C as centre and the same radius draw two arcs on either side of AC to cut the arcs of step 2 at B and D respectively.
4. Join AB, BC, CD and DA.
ABCD is the required rhombus.


Question 3

Construct a quadrilateral ABCD in which AB = 4 cm, BC = 3 cm, AD = 2.5 cm, AC = 4.5 cm and BD = 4 cm.

Solution:

Steps of construction:

1. Draw AB = 4 cm.
2. With A as centre and AD (= 2.5 cm) as radius draw an arc.
3. With B as centre and BD (= 4 cm) as radius draw another arc to cut the arc of step 2 at D.
4. With A as centre and AC (= 4.5 cm) as radius draw an arc.
5. With B as centre and BC (= 3 cm) as radius draw another arc to cut the arc of step 4 at C.
6. Join AD, BC and CD.
ABCD is the required quadrilateral.


Question 4

Construct a quadrilateral ABCD in which BC = 7.5 cm, AC = AD = 6 cm, CD = 5 cm and BD =10 cm.


Solution:

Steps of construction:

1. Draw BC = 7.5 cm.
2. With B as centre and BD (= 10cn) draw an arc.
3. With C as centre and CD (= 5 cm) as radius draw another arc to cut the arc of step 2 at D.
4. With C as centre and CA (= 6 cm) draw an arc.
5. With D as centre and DA (= 6 cm) draw another arc to cut the arc of step 4 at A.
6. Join AB, CD and AD.
ABCD is the required quadrilateral.


Question 5

Construct a quadrilateral ABCD in which AB = 5.5 cm, BC = 4 cm, A = 60°, B = 105° and C = 105°.


Solution:

Steps of construction:

1. Draw AB = 5.5 cm.
2. At A construct an angle BAA’ of measure 60
° .
3. At B, using a protractor, draw an angle ABB’ of measure 105
° .
4. With B as centre mark BC = 4 cm on BB’.
5. At C, using a protractor, draw an angle BCC’ of measure 105
° .
6. CC’ intersects AA’ at D.
ABCD is the required quadrilateral.


Question 6

Construct a quadrilateral ABCD in which BC = 5.5 cm, CD = 4 cm, A = 70°, B = 110° and D = 85°.


Solution:
C = 360° - ( A + B + D)
      = 360
° - (70° + 110° + 85°)
      = 360
° - 255°
      = 105°

Steps of construction:

1. Draw BC = 5.5 cm.
2. At B, draw an angle BCC’ of measure 105
° using a protractor.
3. With C as centre draw an arc on CC’ such that CD = 4 cm.
4. At D, draw an angle of measure 85
° using a protractor.
5. At B, draw an angle BCC’ of measure 110
° using a protractor to cut DD’ at A.
ABCD is the required quadrilateral.


Question 7

Construct a parallelogram whose two sides and one angle are 4 cm, 5.5 cm and 700 respectively.


Solution:

P = 70°
∴ ∠ Q = 180° - 70° = 110°
Steps of construction:

1. Draw PQ = 4 cm.
2. At P, draw an angle QPP’ of measure 70
° .
3. With P as centre and PS (= 5.5 cm) as radius draw an arc on PP’ to cut PP’ at S.
4. At Q, draw an angle of PQQ’ of measure 110
° .
7. With Q as centre and QR (= 5.5 cm) as radius draw an arc on QQ’ to cut QQ’ at R.
5. Join SR.
PQRS is the required parallelogram.


Question 8

Construct a quadrilateral PQRS in which PQ = 3.5 cm, QR = 2.5 cm, RS = 4 cm, Q = 75° and R = 120°.


Solution:

Steps of construction:

1. Draw QR = 2.5 cm.
2. At Q, construct an angle Q'QQ'' = 30
° .
3. Draw QQ''' the bisector of angle Q'QQ'' to get the angle Q = 75
°
4. Mark a point on QQ''' such that QP = 3.5 cm.
5. At R, construct an angle QRR' = 120
°.
6. Mark a point S on RR' such that RS = 4 cm.
7. Join PS.
PQRS is the required quadrilateral.


Question 9

Construct a rectangle with sides 4.5 cm and 6 cm.

 


Solution:

Steps of construction:

1. Draw AB = 6 cm.
2. At A, draw AA’ perpendicular to AB.
3. With A as centre and AD (= 4.5 cm) as radius draw an arc on AA’ to cut AA’ at D.
4. At B, draw BB’ perpendicular to AB.
5. With B as centre and BC (= 4.5 cm) as radius draw an arc on BB’ to cut BB’ at C.
6. Join CD.
ABCD is the required rectangle.





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