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Chapter: 8th Maths : Chapter 5 : Geometry

Exercise 5.5 (Construction of Special Quadrilaterals: Parallelogram, Rhombus, Rectangle, Square)

8th Maths : Chapter 5 : Geometry : Construction of Special Quadrilaterals, Construction of a Parallelogram, Construction of a Rhombus, Construction of a Rectangle, Construction of a Square

Exercise 5.5

I. Construct the following parallelograms with the given measurements and find their area.

1. ARTS, AR=6cm, RT=5cm and ART = 70º .

2. CAMP, CA=6cm, AP=8cm and CP=5.5cm.

3. EARN, ER=10cm, AN=7cm and EOA =110º where ̅E̅R̅ and  ̅A̅N̅ intersect at O.

4. GAIN, GA=7.5cm, GI=9cm and GAI =100º .

 

1. ARTS, AR=6cm, RT=5cm and ART = 70º .

Solution:

Given : In the Parallelogram ARTS,

AR = 6 cm, RT = 5 cm, and ART = 70°


Construction:

Steps:

1. Draw a line segment AR = 6 cm.

2. Make an angle ART = 70° at R on AR

3. With R as centre, draw an arc of radius 5 cm cutting RX at T

4. Draw a line TY parallel to AR through T.

5. With T as centre, draw an arc of radius 6 cm cutting TY at S. Join AS

6. ARTS is the required parallelogram.

Calculation of area:

Area of the parallelogram ARTS = b × h sq. units

= 6 × 4.7 = 28.2 sq. cm

 

2. CAMP, CA=6cm, AP=8cm and CP=5.5cm.

Solution:

Given : In the Parallelogram CAMP,

CA = 6 cm, AP = 8 cm, and CP = 5.5 cm


Construction:

Steps:

1. Draw a line segment CA = 6 cm.

2. With C as centre, draw an arc of length 5.5 cm

3. With A as centre, draw an arc of length 8 cm

4. Mark the intersecting point of these two arcs as P

5. Draw a line PX parallel to CA

6. With P as centre draw an arc of radius 6 cm cutting PX at M. Join AM

7. CAMP is the required parallelogram.

Calculation of area:

Area of the Parallelogram CAMP = b × h sq. units

= 6 × 5.5 = 33 sq. cm

 

3. EARN, ER=10cm, AN=7cm and EOA =110º where ̅E̅R̅ and ̅A̅N̅ intersect at O.

Solution:

Given : in the parallelogram EARN,

ER = 10 cm, AN = 7 cm, and EOA = 110°

Where E̅R̅ and A̅N̅ intersect at 0


 Construction:

Steps:

1. Draw a line segment PX. Mark a point O on PX

2. Make an angle EOA = 110° on PX at O

3. Draw arcs of radius 3.5 cm with O as centre on either side of PX. Cutting YZ on A and N

4. With A as centre, draw an arc of radius 10 cm, cutting PX at E. Join AE

5. Draw a line parallel to AE at N cutting PX at R. Join EN and AR

6. EARN is the required parallelogram

Calculation of area:

Area of the Parallelogram EARN = b × h sq. units

= 10 × 5.5 = 55 sq. cm

 

4. GAIN, GA=7.5cm, GI=9cm and GAI =100º .

Solution:

Given : In the parallelogram GAIN,

GA = 7.5 cm, GI = 9 cm, and GAI = 100°


Construction:

Steps:

1. Draw a line segment GA = 7.5 cm.

2. Make an angle GAI = 100° at A.

3. With G as centre, draw an arc of radius 9 cm cutting AX at I. Join GI.

4. Draw a line IY parallel to GA through I.

5. With 1 as centre, draw an arc of radius 7.5 cm on IY cutting at N. Join GN

6. GAIN is the required parallelogram.

Calculation of area:

Area of the Parallelogram GAIN = b × h sq. units

= 7.5 × 3.9 = 29.25 sq. cm

 

II. Construct the following rhombuses with the given measurements and also find their area.

(i) FACE, FA= 6 cm and FC = 8 cm

(ii) CAKE, CA=5 cm and A = 65°

(iii) LUCK, LC = 7.8 cm and UK = 6 cm

(iv) PARK, PR = 9 cm and P =70°

 

(i) FACE, FA = 6 cm and FC = 8 cm

Solution:

Given 6 cm and FC = 8 cm


Steps:

(i) Drawn a line segment FA = 6 cm.

(ii) With F and A as centres, drawn arcs of radii 8 cm and 6 cm respectively and let them cut at C.

(iii) Joined FC and AC. 

(iv) With F and C as centres, drawn arcs of radius 6 cm each and let them cut at E.

(v) Joined FE and EC.

(vi) FACE is the required rhombus.

Calculation of Area :

Area of the rhombus = 1/2 × d1 × d2 sq.units = 1/2 × 8 × 9 sq.units = 36 cm2

 

(ii) CAKE, CA = 5 cm and A = 65°

Solution:

Given CA = 5 cm and A = 65°


Steps :

(i) Drawn a line segment CA = 5 cm.

(ii) At A on AC, made CAX = 60°

(iii) With A as centres, drawn arcs of radius 5 cm. let it cut AX at K.

(iii) With K and C as centres, drawn arcs of radius 5 cm each and let them cut at E.

(v) Joined KE and CE.

(vi) CAKE is the required rhombus.

Calculation of Area :

Area of the rhombus = 1/2 × d1 × d2 sq.units

= 1/2 × 5.4 × 8.5 cm2

= 22.95 cm2

 

(iii) LUCK, LC = 7.8 cm and UK = 6 cm

Solution:

Given LC = 7.8 cm and UK = 6 cm


Steps:

(i) Drawn a line segment LC = 7.8 cm.

(ii) Drawn the perpendicular bisector XY to LC. Let it cut LC at 'O'

(iii) With O as centres, drawn arc of radius 3 cm on either side of O which cut OX at K and OY at U.

(iv) Joined LU, UC, CK and LK.

(v) LUCK is the required rhombus.

Calculation of Area :

Area of the rhombus = 1/2 × d1 × d2 sq.units

= 1/2 × 7.8 × 6 cm2  = 23.4 cm2

 

(iv) PARK, PR = 9 cm and P = 70°

Solution:

Given: PR = 9 cm and P = 70°


Steps :

(i) Drawn a line segment PR = 9 cm.

(ii) At P, made RPX = RPY = 35° on either side of PR.

(iii) At R, made PRQ = PRS = 35° on either side of PR

(iv) Let PX and RQ cut at A and PY and RS at K.

(v) PARK is the required rhombus

Calculation of Area :

Area of the rhombus = 1/2 × d1 × d2 sq.units = 1/2 × 9 × 6.2 cm2 

= 27.9 cm2

 

III. Construct the following rectangles with the given measurements and also find their area.

(i) HAND, HA = 7 cm and AN = 4 cm

(ii) LAND, LA = 8 cm and AD = 10 cm

 

(i) HAND, HA = 7 cm and AN = 4 cm

Solution: Given HA = 7 cm and AN = 4 cm


Steps:

(i) Drawn a line segment HA = 7 cm.

(ii) At H, constructed HX HA.

(iii) With H as centre, drawn an arc of radius 4 cm and let it cut at HX at D.

(iv) With A and D as centres, drawn arcs of radii 4 cm and 7 cm respectively and let them cut at N.

(v) Joined AN and DN.

(vi) HAND is the required rectangle.

Calculation of Area :

Area of the rectangle HAND = l × b sq.units

= 7 × 4 cm2

= 28 cm2

 

(ii) LAND, LA = 8 cm and AD = 10 cm

Solution:

Given LA = 8 cm and AD = 10 cm


Steps :

(i) Drawn a line segment LA = 8 cm.

(ii) At L, constructed LX LA.

(iii) With A as centre, drawn an arc of radius 10 cm and let it cut at LX at D.

(iv) With A as centre and LD as radius drawn an arc. Also with D as centre and LA as radius drawn another arc. Let then cut at N.

(v) Joined DN and AN.

(vi) LAND is the required rectangle.

Calculation of Area :

Area of the rectangle LAND = l × b sq.units

= 8 × 5.8 cm2

= 46.4 cm2

 

IV. Construct the following squares with the given measurements and also find their area.

(i) EAST, EA = 6.5 cm

(ii) WEST, WS = 7.5 cm

 

(i) EAST, EA = 6.5 cm

Solution:

Given side = 6.5 cm


Steps :

(i) Drawn a line segment EA = 6.5 cm.

(ii) At E, constructed EX EA.

(iii) With E as centre, drawn an arc of radius 6.5 cm and let it cut EX at T.

(iv) With A and T as centre drawn an arc of radius 6.5 cm each and let them cut at S.

(v) Joined TS and AS.

(vi) EAST is the required square.

Calculation of Area :

Area of the square EAST = a2 sq.units

= 6.5 × 6.5 cm2

= 42.25 cm2

 

(ii) WEST, WS = 7.5 cm

Solution:

Given: diagonal = 7.5 cm


Steps:

(i) Drawn a line segment WS = 7.5 cm.

(ii) Drawn the perpendicular bisector XY to WS. Let it bisect BS at O.

(iii) With O as centre, drawn an arc of radius 3.7 cm on either side of O which cut OX at T and OY at E

(iv) Joined BE, ES, ST and BT.

(v) WEST is the required square.

Calculation of Area :

Area of the square WEST = a2 sq.units

= 5.3 × 5.3 cm2

= 28.09 cm2

 

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8th Maths : Chapter 5 : Geometry : Exercise 5.5 (Construction of Special Quadrilaterals: Parallelogram, Rhombus, Rectangle, Square) | Questions with Answers, Solution | Geometry | Chapter 5 | 8th Maths

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