EXERCISE 17A

(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.

Steps of construction

Step 1: Draw AB = 4.2 cm.

Step 2: with a as centre and radius equal to 8 cm, draw an arc.

Step 3: With B as 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 centre and radius equal to 5 cm, draw an arc.

Step 6: With C as centre and radius equal to 5.2 cm, draw another arc, cutting the previous arc at D.

Step 7: Join AD and CD.

Then, ABCD is the required quadrilateral, shown alongside.

(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.

Steps of construction:

Step 1: Draw PQ = 5.4 cm.

Step 2: with P as centre and radius equal to 4 cm, draw an arc.

Step 3: With Q as 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 centre and radius equal to 3.5 cm, draw an arc.

Step 6: With R as centre and radius equal to 4.3 cm, draw another arc, cutting the previous arc at S.

Step 7: Join PS and RS.

Then, PQRS is the required quadrilateral, shown alongside.

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

Steps of construction

Step 1: Draw AB = 3.5 cm.

Step 2: with B as centre and radius equal to 5.6 cm, draw an arc.

Step 3: With B as centre and radius equal to 3.8 cm, draw another arc, cutting the previous arc at C.

Step 4: Join BC.

Step 5: With A as centre and radius equal to 4.5 cm, draw an arc.

Step 6: With C as centre and radius equal to 4.5 cm, draw another arc, cutting the previous arc at D.

Step 7: Join AD and CD.

Then, ABCD is the required quadrilateral, shown alongside.

(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.

Steps of construction

Step 1: Draw AB = 3.6 cm.

Step 2: with A as centre and radius equal to 4 cm, draw an arc.

Step 3: With B as centre and radius equal to 3.3 cm, draw another arc, cutting the previous arc at C.

Step 4: Join BC.

Step 5: With A as centre and radius equal to 2.7 cm, draw an arc.

Step 6: With B as the centre and radius equal to 4 cm, draw an arc.

Step 7: Join AD and CD.

Then, ABCD is the required quadrilateral, shown alongside.

(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.

Steps of construction:

Step 1: Draw QR = 7.5 cm.

Step 2: with Q as centre and radius equal to 10 cm, draw an arc.

Step 3: With R as centre and radius equal to 5 cm, draw another arc, cutting the previous arc at S.

Step 4: Join RS.

Step 5: With R as centre and radius equal to 6 cm, draw an arc.

Step 6: With S as centre and radius equal to 6 cm, draw another arc, cutting the previous arc at P.

Step 7: Join PS and PQ.

Then, PQRS is the required quadrilateral, shown alongside.

And the length of PQ is 4.8 cm.

(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.

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 8cm, 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.

Then, ABCD is the required quadrilateral.

(7) Construct a quadrilateral ABCD in which AB = BC = 3.5 cm, AD = CD = 5.2 cm and ∠ABC = 120^o.

Steps of construction:

Step 1: Draw AB = 3.5 cm.

Step 2: Make ∠ABC = 120^o

Step 3: With B as the centre, draw an arc 3.5 cm and join BC.

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 cutting the previous arc at D.

Step 6: join CD and AD.

Thus, ABCD is required quadrilateral.

(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^o.

Steps of construction:

Step 1: Draw AB = 2.9 cm.

Step 2: make a 70^o angle.

Step 3: With A as the centre, draw an arc of radius 3.4 cm. Name the point D.

Step 4: With D as the centre draw an arc 2.7 cm. name the point as C.

Step 5: With B as the centre draw an arc of radius 3.2 cm, cutting the previous arc at C.

Step 6: Join BC and CD.

Then, ABCD is the required quadrilateral.

(9) Construct a quadrilateral ABCD in which AB = 3.5 cm, BC = 5 cm, CD = 4.6 cm, ∠B = 125^o and ∠C = 60^o.

Steps of construction:

Step 1: Draw BC = 5 cm.

Step 2: Make a angle at B 125^o and at C 60^o.

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 radius 4.6 cm. Name the point as D.

Step 5: Join A and D.

Then, ABCD is the required quadrilateral.

(10) Construct a quadrilateral PQRS in which PQ = 6 cm, QR = 5.6 cm, RS = 2.7 cm, ∠Q = 45^o and ∠R = 90^o.

Steps of construction:

Step 1: Draw QR = 5.6 cm.

Step 2: Make a angle Q = 45^o and angle R = 90^o

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 2.7 cm. Name that point as S.

Step 5: Join P and S.

Then, PQRS is the required quadrilateral.

(11) Construct a quadrilateral ABCD in which AB = 5.6 cm, BC = 4 cm, ∠A = 50^o, ∠B = 105^o and ∠D = 80^o.

Steps of construction:

Steps 1: Draw AB = 5.6 cm

Step 2: Make ∠A = 50^o and ∠B = 105^o

Step 3: With B as the centre, draw an arc of 4 cm

Step 4: Sum of all the angles of the quadrilateral is 360^o.

∠A + ∠B + ∠C + ∠D = 360

⇒ 50 + 105 + ∠C + 80 = 360

⇒ ∠C = 360 – 235

⇒ ∠C = 125

Step 5: With C as the centre, make a angle of measure 125^o

Step 6: Join C and D.

Step 7: Measure ∠D = 80^o.

Then, ABCD is the Quadrilateral.

(12) Construct a quadrilateral PQRS in which PQ = 5 cm, QR = 6.5 cm, ∠P = ∠R = 100^o and ∠S = 75^o.

Steps of construction:

Step 1: Draw PQ = 5 cm.

Step 2: We have,

∠P + ∠Q + ∠R + ∠S = 360

⇒ 100 + ∠Q + 100 + 75 = 360

⇒ ∠Q = 360 – 275 = 85

Step 3: Make ∠P = 100^o and ∠Q = 85^o

Step 4: With Q as the centre, draw an arc of 6.5 cm

Step 5: Make ∠R = 100^o

Step 6: Join R and S.

Step 7: Measure ∠S = 75^o

Then, PQRS is the required quadrilateral.

(13) Construct a quadrilateral ABCD in which AB = 4 cm, AC = 5 cm, AD = 5.5 cm and ∠ABC = ∠ADC = 90^o.

Steps of construction:

Step 1: Draw AB = 4 cm

Step 2: Make ∠B = 90^o

Step 3: AC² = AB² + BC²

⇒ 25 = 16 + BC²

⇒ BC² = 25 – 16

⇒ BC = √9 = 3 cm.

Step 4: With B as the centre, draw an arc equal to 3 cm.

Step 5: Make ∠C = 90^o

Step 6: With A as the centre and radius equal to 5.5 cm, draw an arc and name the point as D.

Then, ABCD is the required quadrilateral.