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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