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Chapter 14

Construction of Quadrilaterals — Exercise 14.1

Class - 8 ML Aggarwal Understanding ICSE Mathematics

Exercise 14.1

Question 1

Construct a quadrilateral PQRS where PQ = 4.5 cm, QR = 6 cm, RS = 5.5 cm, PS = 5 cm and PR = 6.5 cm

Answer

Given, in quadrilateral PQRS, PQ = 4.5 cm, QR = 6 cm, RS = 5.5 cm, PS = 5 cm and PR = 6.5 cm.

Steps of construction :

  1. Draw a line segment PQ = 4.5 cm.

  2. With Q as centre and radius 6 cm, draw an arc.

  3. With P as centre and radius 6.5 cm, draw another arc cutting the previous arc at R.

  4. Join QR and PR.

  5. With P as centre and radius 5 cm, draw an arc on the side of PR opposite to that of Q.

  6. With R as centre and radius 5.5 cm, draw another arc cutting the previous arc at S.

  7. Join PS and RS.

Construct a quadrilateral PQRS where PQ = 4.5 cm, QR = 6 cm, RS = 5.5 cm, PS = 5 cm and PR = 6.5 cm. Construction of Quadrilaterals, ML Aggarwal Understanding Mathematics Solutions ICSE Class 8

Hence, PQRS is the required quadrilateral.

Question 2

Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 5 cm, CD = 5.6 cm, DA = 4 cm and BD = 5.4 cm

Answer

Given, in quadrilateral ABCD, AB = 3.5 cm, BC = 5 cm, CD = 5.6 cm, DA = 4 cm and BD = 5.4 cm.

Steps of construction :

  1. Draw a line segment AB = 3.5 cm.

  2. With A as centre and radius 4 cm, draw an arc.

  3. With B as centre and radius 5.4 cm, draw another arc cutting the previous arc at D.

  4. Join AD and BD.

  5. With B as centre and radius 5 cm, draw an arc on the side of BD opposite to that of A.

  6. With D as centre and radius 5.6 cm, draw another arc cutting the previous arc at C.

  7. Join BC and CD.

Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 5 cm, CD = 5.6 cm, DA = 4 cm and BD = 5.4 cm. Construction of Quadrilaterals, ML Aggarwal Understanding Mathematics Solutions ICSE Class 8

Hence, ABCD is the required quadrilateral.

Question 3

Construct a quadrilateral PQRS in which PQ = 3 cm, QR = 2.5 cm, PS = 3.5 cm, PR = 4 cm and QS = 5 cm

Answer

Given, in quadrilateral PQRS, PQ = 3 cm, QR = 2.5 cm, PS = 3.5 cm, PR = 4 cm and QS = 5 cm.

Steps of construction :

  1. Draw a line segment PQ = 3 cm.

  2. With P as centre and radius 4 cm, draw an arc.

  3. With Q as centre and radius 2.5 cm, draw another arc cutting the previous arc at R.

  4. Join PR and QR.

  5. With P as centre and radius 3.5 cm, draw an arc on the side of PR opposite to that of Q.

  6. With Q as centre and radius 5 cm, draw another arc cutting the previous arc at S.

  7. Join PS, RS and QS.

Construct a quadrilateral PQRS in which PQ = 3 cm, QR = 2.5 cm, PS = 3.5 cm, PR = 4 cm and QS = 5 cm. Construction of Quadrilaterals, ML Aggarwal Understanding Mathematics Solutions ICSE Class 8

Hence, PQRS is the required quadrilateral.

Question 4

Construct a quadrilateral ABCD such that BC = 5 cm, AD = 5.5 cm, CD = 4.5 cm, AC = 7 cm and AB = 5.5 cm

Answer

Given, in quadrilateral ABCD, BC = 5 cm, AD = 5.5 cm, CD = 4.5 cm, AC = 7 cm and AB = 5.5 cm.

Steps of construction :

  1. Draw a line segment AC = 7 cm.

  2. With A as centre and radius 5.5 cm, draw an arc.

  3. With C as centre and radius 4.5 cm, draw another arc cutting the previous arc at D.

  4. Join AD and CD.

  5. On the opposite side of AC, with A as centre and radius 5.5 cm, draw an arc.

  6. With C as centre and radius 5 cm, draw another arc cutting the previous arc at B.

  7. Join AB and CB.

Construct a quadrilateral ABCD such that BC = 5 cm, AD = 5.5 cm, CD = 4.5 cm, AC = 7 cm and AB = 5.5 cm. Construction of Quadrilaterals, ML Aggarwal Understanding Mathematics Solutions ICSE Class 8

Hence, ABCD is the required quadrilateral.

Question 5

Construct a quadrilateral ABCD given that BC = 6 cm, CD = 4 cm, ∠B = 45°, ∠C = 90° and ∠D = 120°

Answer

Given, in quadrilateral ABCD, BC = 6 cm, CD = 4 cm, ∠B = 45°, ∠C = 90° and ∠D = 120°.

Steps of construction :

  1. Draw a line segment BC = 6 cm.

  2. At C, construct ∠BCX = 90°.

  3. From CX, cut off CD = 4 cm.

  4. At D, construct ∠CDY = 120°.

  5. At B, construct ∠CBZ = 45° such that BZ meets DY at A.

Construct a quadrilateral ABCD given that BC = 6 cm, CD = 4 cm, ∠B = 45°, ∠C = 90° and ∠D = 120°. Construction of Quadrilaterals, ML Aggarwal Understanding Mathematics Solutions ICSE Class 8

Hence, ABCD is the required quadrilateral.

Question 6

Construct a quadrilateral PQRS where PQ = 4 cm, QR = 6 cm, ∠P = 60°, ∠Q = 90° and ∠R = 120°

Answer

Given, in quadrilateral PQRS, PQ = 4 cm, QR = 6 cm, ∠P = 60°, ∠Q = 90° and ∠R = 120°.

Steps of construction :

  1. Draw a line segment PQ = 4 cm.

  2. At Q, construct ∠PQX = 90°.

  3. From QX, cut off QR = 6 cm.

  4. At R, construct ∠QRY = 120°.

  5. At P, construct ∠QPZ = 60° such that PZ meets RY at S.

Construct a quadrilateral PQRS where PQ = 4 cm, QR = 6 cm, ∠P = 60°, ∠Q = 90° and ∠R = 120°. Construction of Quadrilaterals, ML Aggarwal Understanding Mathematics Solutions ICSE Class 8

Hence, PQRS is the required quadrilateral.

Question 7

Construct a quadrilateral ABCD such that AB = 5 cm, BC = 4.2 cm, AD = 3.5 cm, ∠A = 90° and ∠B = 60°

Answer

Given, in quadrilateral ABCD, AB = 5 cm, BC = 4.2 cm, AD = 3.5 cm, ∠A = 90° and ∠B = 60°.

Steps of construction :

  1. Draw a line segment AB = 5 cm.

  2. At A, construct ∠BAX = 90°.

  3. From AX, cut off AD = 3.5 cm.

  4. At B, construct ∠ABY = 60° on the same side of AB as that of D.

  5. From BY, cut off BC = 4.2 cm.

  6. Join CD.

Construct a quadrilateral ABCD such that AB = 5 cm, BC = 4.2 cm, AD = 3.5 cm, ∠A = 90° and ∠B = 60°. Construction of Quadrilaterals, ML Aggarwal Understanding Mathematics Solutions ICSE Class 8

Hence, ABCD is the required quadrilateral.

Question 8

Construct a quadrilateral PQRS where PQ = 4 cm, QR = 5 cm, RS = 4.5 cm, ∠Q = 60° and ∠R = 90°

Answer

Given, in quadrilateral PQRS, PQ = 4 cm, QR = 5 cm, RS = 4.5 cm, ∠Q = 60° and ∠R = 90°.

Steps of construction :

  1. Draw a line segment QR = 5 cm.

  2. At Q, construct ∠RQX = 60°.

  3. From QX, cut off QP = 4 cm.

  4. At R, construct ∠QRY = 90° on the same side of QR as that of P.

  5. From RY, cut off RS = 4.5 cm.

  6. Join PS.

Construct a quadrilateral PQRS where PQ = 4 cm, QR = 5 cm, RS = 4.5 cm, ∠Q = 60° and ∠R = 90°. Construction of Quadrilaterals, ML Aggarwal Understanding Mathematics Solutions ICSE Class 8

Hence, PQRS is the required quadrilateral.

Question 9

Construct a quadrilateral BEST where BE = 3.8 cm, ES = 3.4 cm, ST = 4.5 cm, TB = 5 cm and ∠E = 80°

Answer

Given, in quadrilateral BEST, BE = 3.8 cm, ES = 3.4 cm, ST = 4.5 cm, TB = 5 cm and ∠E = 80°.

Steps of construction :

  1. Draw a line segment BE = 3.8 cm.

  2. At E, construct ∠BEX = 80°.

  3. From EX, cut off ES = 3.4 cm.

  4. With S as centre and radius 4.5 cm, draw an arc.

  5. With B as centre and radius 5 cm, draw another arc cutting the previous arc at T.

  6. Join ST and TB.

Construct a quadrilateral BEST where BE = 3.8 cm, ES = 3.4 cm, ST = 4.5 cm, TB = 5 cm and ∠E = 80°. Construction of Quadrilaterals, ML Aggarwal Understanding Mathematics Solutions ICSE Class 8

Hence, BEST is the required quadrilateral.

Question 10

Construct a quadrilateral ABCD where AB = 4.5 cm, BC = 4 cm, CD = 3.9 cm, AD = 3.2 cm and ∠B = 60°

Answer

Given, in quadrilateral ABCD, AB = 4.5 cm, BC = 4 cm, CD = 3.9 cm, AD = 3.2 cm and ∠B = 60°.

Steps of construction :

  1. Draw a line segment AB = 4.5 cm.

  2. At B, construct ∠ABX = 60°.

  3. From BX, cut off BC = 4 cm.

  4. With A as centre and radius 3.2 cm, draw an arc.

  5. With C as centre and radius 3.9 cm, draw another arc cutting the previous arc at D.

  6. Join AD and CD.

Construct a quadrilateral ABCD where AB = 4.5 cm, BC = 4 cm, CD = 3.9 cm, AD = 3.2 cm and ∠B = 60°. Construction of Quadrilaterals, ML Aggarwal Understanding Mathematics Solutions ICSE Class 8

Hence, ABCD is the required quadrilateral.

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