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## Tamilnadu Samacheer Kalvi 8th Maths Solutions Term 2 Chapter 3 Geometry Ex 3.4

Question I.

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

Question 1.

ARTS, AR = 6 cm, RT = 5 cm and ∠ART = 70°.

Solution:

Given:

In the Parallelogram ARTS,

AR = 6 cm

RT = 5 cm and ∠ART = 70°

Construction:

Steps:

- Draw a line segment AR = 6 cm.
- Make an angle ∠ART = 70° at R on AR
- With R as centre, draw an arc of radius 5 cm cutting RX at T
- Draw a line TY parallel to AR through T.
- With T as centre, draw an arc of radius 6 cm cutting TY at S. Join AS
- ARTS is the required parallelogram.

Calculation of area:

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

= 6 x 4.7 = 28.2 sq. cm

Question 2.

BANK, BA = 7 cm, BK = 5.6 cm and ∠KBA = 85°.

Solution:

Given:

In the parallelogram BANK, BA =7 cm, BK = 5.6 cm, and ∠KBA = 85°

Construction:

Steps:

- Draw a line segment KB = 5.6 cm.
- Make an angle ∠KBA = 85° at B
- Draw an arc of radius 7 cm with B as centre on BX.
- Draw a line AY parallel to KB.
- With A as centre, draw an arc of radius 5.6 cm cutting AY at N. Join KN
- BANK is the required parallelogram.

Calculation of area:

Area of the Parallelogram BANK = b x h sq. units

= 5.6 x 7 = 39.2 sq. cm

Question 3.

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

Solution:

Given:

In the parallelogram CAMP,

CA = 6 cm

AP = 8 cm, and CP = 5.5cm

Construction:

Steps:

- Draw a line segment CA = 6 cm.
- With C as centre, draw an arc of length 5.5 cm
- With A as centre, draw an arc of length 8 cm
- Mark the intersecting point of these two arcs as P
- Draw a line PX parallel to CA
- With P as centre draw an arc of radius 6 cm cutting PX at M. Join AM
- CAMP is the required parallelogram.

Calculation of area:

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

= 6 x 5.5 = 33 sq. cm

Question 4.

DRUM, DR = 7 cm, RU = 5.5 cm and DU = 8 cm.

Solution:

Given:

In the parallelogram DRUM,

DR = 7 cm,

RU = 5.5 cm, and DU = 8 cm

Construction:

Steps:

- Draw a line segment DR = 7 cm.
- With D and R as centres, draw arcs of radii 8 cm and 5.5 cm.
- Mark the intersecting point of these arcs as U. Join DU and RU
- Draw a line UX parallel to DR through U.
- With U as centre draw an arc of radius 7 cm cutting UX at M. Join DM
- DRUM is the required parallelogram.

Calculation of area:

Area of the Parallelogram DRUM = b x h sq. units

= 7 x 5.4 = 37.8 sq. cm

Question 5.

EARN, ER = 10 cm, AN = 7 cm and ∠EOA 110° where \(\overline { ER } \) and \(\overline { AN } \) intersect at O.

Solution:

Given:

In the parallelogram EARN,

ER= 10 cm

AN = 7 cm, and ∠EOA = 110°

Construction:

Steps:

- Draw a line segment PX. Mark a {Joint O on PX
- Make an angle ∠EOA = 110° on PX at O
- Draw arcs of radius 3.5 cm with O as centre on either side of PX. Cutting YZ on A and N
- With A as centre, draw an arc of radius 10 cm, cutting PX at E. Join AE
- Draw a line parallel to AE at N cutting PX at R. Join EN and AR
- EARN is the required parallelogram

Calculation of area:

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

= 10 x 5.5 = 55 sq. cm

Question 6.

FAIR, FI = 8 cm, AR = 6 cm and ∠IOR = 80° where \(\overline { FI } \) and \(\overline { AR } \) intersect at O.

Solution:

Given:

In the parallelogram FAIR,

FI = 8cm

AR = 6 cm and ∠IOR = 80°, where \(\overline { FI } \) and \(\overline { AR } \) intersect at O

Construction:

Steps:

- Draw a line segment \(\overline { FI } \) = 8 cm
- Mark O the midpoint of \(\overline { FI } \)
- Draw a line \(\overline { XY } \) through O which makes ∠IOX = 80°
- With O as centre and 3 cm as radius draw two arcs on XY on either sides of \(\overline { FI } \). Let the arcs cut \(\overline { OX } \) at R and \(\overline { OY } \) at A
- Join \(\overline { IR } \), \(\overline { FR } \), \(\overline { FA } \) and \(\overline { AI } \)
- FAIR is the required parallelogram

Calculation of area:

Area of the Parallelogram FAIR = b x h sq. units

= 5.4 x 4.3 = 23.22 sq. cm

Question 7.

GAIN, GA = 7.5 cm, GI = 9 cm and ∠GAI – 100°

Solution:

Given:

In the parallelogram GAIN,

GA = 7.5 cm

GI = 9 cm and ∠GAI= 100°

Construction:

Steps:

- Draw a line segment GA = 7.5 cm.
- Make an angle GAI = 100° at A.
- With G as centre, draw an arc of radius 9 cm cutting AX at I. Join GI.
- Draw a line IY parallel to GA through I.
- With I as centre, draw an arc of radius T.5 cm on IY cutting at N. Join GN
- GAIN is the required parallelogram.

Calculation of area:

Area of Parallelogram GAIN = b x h sq.units

= 7.5 x 3.9 = 29.25 sq. cm

Question 8.

HERB, HE = 6 cm, ∠EHB = 60° and EB = 7 cm.

Solution:

Given:

In the parallelogram HERB,

HE = 6 cm, ∠EHB = 60° and

EB = 7 cm

Construction:

Steps:

- Draw a line segment HE = 6 cm.
- Make an angle ∠BHE = 60° at H.
- With E as centre, draw an arc of radius 7 cm cutting HX at B.
- Draw a line BY parallel to HE through B.
- Draw an arc of radius 6 cm with B as centre, cutting BY at R. Join ER.
- HERB is the required parallelogram.

Calculation of area:

Area of the Parallelogram HERB = b x h sq. units

= 6 x 6.7 = 40.2 sq. cm