RS Aggarwal solution class 8 chapter 17 Construction of Quadrilaterals Exercise 17A

Exercise 17A

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Q1 | Ex-17A | Class 8 | RS AGGARWAL | chapter 17 | Construction of Quadrilaterals

Question 1:

Construct a quadrilateral ABCD in which AB = 4.2 cm, BC = 6 cm, CD = 5.2 cm, DA = 5 cm and AC = 8 cm.

Answer 1:

Steps of construction:
Step 1: Draw AB=4.2 cm.
Step 2: With A as the centre and radius equal to 8 cm, draw an arc.
Step 3: With B as the centre and radius equal to 6 cm, draw another arc, cutting the previous arc at C.
Step 4: Join BC.
Step 5: With A as the centre and radius equal to 5 cm, draw an arc.
Step 6: With C as the centre and radius equal to 5.2 cm, draw another arc, cutting the previous arc at D.
Step 7: Join AD and CD.

Thus, ABCD is the required quadrilateral.










Q2 | Ex-17A | Class 8 | RS AGGARWAL | chapter 17 | Construction of Quadrilaterals

Question 2:

Construct a quadrilateral PQRS in which PQ = 5.4 cm, QR = 4.6 cm, RS = 4.3 cm, SP = 3.5 cm and diagonal PR = 4 cm.

Answer 2:

Steps of construction:
Step 1: Draw PQ=5.4 cm.
Step 2: With P as the centre and radius equal to 4 cm, draw an arc.
Step 3: With Q as the centre and radius equal to 4.6 cm, draw another arc, cutting the previous arc at R.
Step 4: Join QR.
Step 5: With P as the centre and radius equal to 3.5 cm, draw an arc.
Step 6: With R as the centre and radius equal to 4.3 cm, draw another arc, cutting the previous arc at S.
Step 7: Join PS and RS.

Thus, PQRS is the required quadrilateral.








Q3 | Ex-17A | Class 8 | RS AGGARWAL | chapter 17 | Construction of Quadrilaterals

Question 3:

Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 3.8 cm, CD = DA = 4.5 cm and diagonal BD = 5.6 cm.

Answer 3:

Steps of construction:
Step 1: Draw AB=3.5 cm.
Step 2: With B as the centre and radius equal to 5.6 cm, draw an arc.
Step 3: With A as the centre and radius equal to 4.5 cm, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With D as the centre and radius equal to 4.5 cm, draw an arc.
Step 6: With B as the centre and radius equal to 3.8 cm, draw another arc, cutting the previous arc at C.
Step 7: Join BC and CD.

Thus, ABCD is the required quadrilateral.








Q4 | Ex-17A | Class 8 | RS AGGARWAL | chapter 17 | Construction of Quadrilaterals

Question 4:

Construct a quadrilateral ABCD in which AB = 3.6 cm, BC = 3.3 cm, AD = 2.7 cm, diagonal AC = 4.6 cm and diagonal BD = 4 cm.

Answer 4:

Steps of construction:
Step 1: Draw AB=3.6 cm.
Step 2: With B as the centre and radius equal to 4 cm, draw an arc.
Step 3: With A as the centre and radius equal to 2.7 cm, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to 4.6 cm, draw an arc.
Step 6: With B as the centre and radius equal to 3.3 cm, draw another arc, cutting the previous arc at C.
Step 7: Join AC, BC and CD.

Thus, ABCD is the required quadrilateral.










Q5 | Ex-17A | Class 8 | RS AGGARWAL | chapter 17 | Construction of Quadrilaterals

Question 5:

Construct a quadrilateral PQRS in which QR = 7.5 cm, PR = PS = 6 cm, RS = 5 cm and QS = 10 cm. Measure the fourth side.

Answer 5:


Steps of construction:
Step 1: Draw QR=7.5 cm.
Step 2: With Q as the centre and radius equal to 10 cm, draw an arc.
Step 3: With R as the centre and radius equal to 5 cm, draw another arc, cutting the previous arc at S.
Step 4: Join QS and RS.
Step 5: With S as the centre and radius equal to 6 cm, draw an arc.
Step 6: With R as the centre and radius equal to 6 cm, draw another arc, cutting the previous arc at P.
Step 7: Join PS and PR.
Step 8: PQ = 4.9 cm
Thus, PQRS is the required quadrilateral.









Q6 | Ex-17A | Class 8 | RS AGGARWAL | chapter 17 | Construction of Quadrilaterals

Question 6:

construct a quadrilateral ABCD in which AB =3.4 cm, CD = 3 cm, DA = 5.7 cm, AC = 8 cm and BD = 4 cm.

Answer 6:

Steps of construction:
Step 1: Draw AB=3.4 cm.
Step 2: With B as the centre and radius equal to 4 cm, draw an arc.
Step 3: With A as the centre and radius equal to 5.7 cm, draw another arc, cutting the previous arc at D.
Step 4: Join BD and AD.
Step 5: With A as the centre and radius equal to 8 cm, draw an arc.
Step 6: With D as the centre and radius equal to 3 cm, draw another arc, cutting the previous arc at C.
Step 7: Join AC, CD and BC.

Thus, ABCD is the required quadrilateral.








Q7 | Ex-17A | Class 8 | RS AGGARWAL | chapter 17 | Construction of Quadrilaterals

Question 7:

Construct a quadrilateral ABCD in which AB = BC = 3.5 cm, AD = CD = 5.2 cm and ∠ABC = 120°.

Answer 7:

Steps of construction:
Step 1: Draw AB3.5 cm.
Step 2: Make ABC=120.
Step 3: With B as the centre, draw an arc 3.5 cm and name that point C.
Step 4: With C as the centre, draw an arc 5.2 cm.
Step 5: With A as the centre, draw another arc ​5.2 cm, cutting the previous arc at D.
Step 6: Join CD and AD.
Thus, ABCD is the required quadrilateral.











Q8 | Ex-17A | Class 8 | RS AGGARWAL | chapter 17 | Construction of Quadrilaterals

Question 8:

Construct a quadrilateral ABCD in which AB = 2.9 cm, BC = 3.2 cm, CD = 2.7 cm, DA = 3.4 cm and ∠A = 70°.

Answer 8:

Steps of construction:
Step 1: Draw AB2.9cm
Step 2: Make A=70
Step 3: With A as the centre, draw an arc of 3.4cm. Name that point as D.
Step 4: With D as the centre, draw an arc of 2.7cm.
Step 5: With B as the centre, draw an arc of 3.2 cm, cutting the previous arc at C.
Step 6: Join CD and BC.
Then, ABCD is the required quadrilateral.









Q9 | Ex-17A | Class 8 | RS AGGARWAL | chapter 17 | Construction of Quadrilaterals

Question 9:

Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 5 cm, CD = 4.6 cm, ∠B = 125° and ∠C = 60°.

Answer 9:

Steps of construction:
Step 1: Draw BC5cm
Step 2: Make B=125 and C=60
Step 3: With B as the centre, draw an arc of 3.5 cm. Name that point as A.
Step 4: With C as the centre, draw an arc of 4.6 cm. Name that point as D.
Step 5: Join A and D.
Then, ABCD is the required quadrilateral.











Q10 | Ex-17A | Class 8 | RS AGGARWAL | chapter 17 | Construction of Quadrilaterals

Question 10:

Construct a quadrilateral PQRS in which PQ = 6 cm, QR = 5.6 cm, RS = 2.7 cm, ∠Q = 45° and ∠R = 90°.

Answer 10:

Steps of construction:
Step 1: Draw QR5.6 cm
Step 2: Make Q=45 and R=90
Step 3: With Q as the centre, draw an arc of 6 cm. Name that point as P.
Step 4: With R as the centre, draw an arc of 2.7cm. Name that point as S.
Step 6: Join P and S.
Then, PQRS is the required quadrilateral.









Q11 | Ex-17A | Class 8 | RS AGGARWAL | chapter 17 | Construction of Quadrilaterals

Question 11:

Construct a quadrilateral ABCD in which AB = 5.6 cm, BC = 4 cm, ∠A = 50°, ∠B = 105° and ∠D = 80°.

Answer 11:

Steps of construction:
Step 1: Draw AB5.6 cm
Step 2: Make A=50 and B=105
Step 3: With B as the centre, draw an arc of 4cm.
Step 3: Sum of all the angles of the quadrilateral is 360.
A+B+C+D=36050+105+C+80=360235+C=360C=360-235C=125
Step 5: With C as the centre, make C equal to 125.
Step 6: Join C and D.
Step 7: Measure D=80
Then, ABCD is the required quadrilateral.










Page-199

Q12 | Ex-17A | Class 8 | RS AGGARWAL | chapter 17 | Construction of Quadrilaterals

Question 12:

Construct a quadrilateral PQRS in which PQ = 5 cm, QR = 6.5 cm, ∠P = ∠R = 100° and ∠S = 75°.

Answer 12:


Steps of construction:
Step 1: Draw PQ5cm
Step 2:
P+Q+R+S=360100+Q+100+75=360275+Q=360Q=360-275Q=85
Step 3: Make P=100 and Q=85
Step 3: With Q as the centre, draw an arc of 6.5 cm.
Step 4: Make R=100
Step 6: Join R and S.
Step 7: Measure S=75
Then, PQRS is the required quadrilateral.










Q13 | Ex-17A | Class 8 | RS AGGARWAL | chapter 17 | Construction of Quadrilaterals

Question 13:

Construct a quadrilateral ABCD in which AB = 4 cm, AC = 5 cm, AD = 5.5 cm and ∠ABC = ∠ACD = 90°.

Answer 13:

Steps of construction:
Step 1: Draw AB=4cm
Step 2: Make B=90
Step 3: AC2=AB2+BC252=42+BC225-16=BC2BC=3cm
With B as the centre, draw an arc equal to 3 cm.
Step 4: Make C=90
Step 5: With A as the centre and radius equal to 5.5 cm, draw an arc and name that point as D.
Then, ABCD is the required quadrilateral.


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