Home | | **Maths 8th Std** | 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=6 cm, RT=5cm and **

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

**3. EARN, ER=10 cm, AN=7cm and **

**4. GAIN, GA=7.5 cm, GI=9cm and **

** **

**1. ARTS, AR=6 cm, RT=5cm and **

**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=6 cm, 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=10 cm, AN=7cm and **

**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=7.5 cm, GI=9cm and **

**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 **

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

**(iv) PARK, PR = 9 cm and **

** **

**(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 × *d*_{1} × *d*_{2}
sq.units = 1/2 × 8 × 9 sq.units = 36 cm^{2}

** **

**(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 × *d*_{1} × *d*_{2}
sq.units

= 1/2 × 5.4 × 8.5 cm^{2}

= 22.95 cm^{2}

** **

**(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 × *d*_{1} × *d*_{2}
sq.units

= 1/2 × 7.8 × 6 cm^{2}
= 23.4 cm^{2}

** **

**(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 × *d*_{1} × *d*_{2}
sq.units = 1/2 × 9 × 6.2 cm^{2}

= 27.9 cm^{2}

** **

**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 cm^{2}

= 28 cm^{2}

** **

**(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 cm^{2}

= 46.4 cm^{2}

** **

**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 = *a*^{2} sq.units

= 6.5 × 6.5 cm^{2}

= 42.25 cm^{2}

** **

**(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 = *a*^{2} sq.units

= 5.3 × 5.3 cm^{2}

= 28.09 cm^{2}

** **

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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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