8th Maths : Chapter 5 : Geometry : Exercise 5.4 : Construction of Quadrilaterals and Construction of Trapeziums

**Exercise
5.4**

** **

**I. Construct the following quadrilaterals
with the given measurements and also find their area.**

**1. ABCD, AB = 5 cm, BC = 4.5 cm, CD = 3.8
cm, DA = 4.4 cm and AC= 6.2 cm.**

**Solution:**

**Given** :

AB = 5 cm, BC = 4.5 cm, CD = 3.8 cm, DA = 4.4 cm, AC= 6.2
cm

**Steps:**

1. Draw a line segment AB = 5 cm

2. With A and B as centers drawn arcs of radii 6.2 cm and 4.5cm
respectively and let them cut at C.

3. Joined AC and BC.

4. With A and C as centrers drawn arcs of radii 4.4cm and 3.8 cm
respectively and let them at D.

5. Joined AD and CD.

6. ABCD is the required quadrilateral.

**Calculation of Area:**

Area of the quadrilateral ABCD = 1/2 × *d* × (*h*_{1}
+ *h*_{2}) sq. units

= 1/2 × 6.2 × (2.6 + 3.6) cm^{2} = 3.1 × 6.2 = 19.22 cm^{2}

**2. PLAY, PL= 7 cm, LA = 6 cm, AY= 6 cm, PA = 8 cm and LY = 7 cm.**

**Solution:**

**Given **

PL = 7 cm, LA = 6 cm, AY= 6 cm, PA = 8 cm, LY = 7 cm

**Steps:**

1. Drawn a line segment PL = 7 cm

2. With P and L as centers, drawn arcs of radii 8 cm and 6 cm
respectively, let them cut at A.

3. Joined PA and LA.

4. With L and A as centers, drawn arcs of radii 7 cm and 6 cm
respectively and let them cut at Y.

5. Joined LY, PY and AY.

6. PLAY is the required quadrilateral.

**Calculation of Area:**

Area of the quadrilateral PLAY = 1/2 × *d* × (*h*_{1}
+ *h*_{2}) sq. units = 1/2 × 8 × (5.1 + 1.4) cm^{2}

= 1/2 × 8 × 6.5 cm^{2}
= 26 cm^{2}

Area of the quadrilateral = 26 cm^{2}

^{}

**3. PQRS, PQ=QR= 3.5 cm, RS= 5.2 cm, SP = 5.3 cm and **

**Solution:**

**Given: **

PQ = QR − 3.5 cm, RS = 5.2 cm, SP = 5.3 cm , ∠Q =120°

**Steps:**

1. Draw a line segment PQ = 3.5 cm

2. Made ∠Q = 120°. Drawn the ray QX.

3. With Q as centre drawn an arc of radius 3.5 cm. Let it cut
the ray QX at R.

4. With R and P as centres drawn arcs of radii 5.2 cm
respectively and let them cut at S.

5. Joined PS and RS.

6. PQRS is the required quadrilateral.

**Calculation of Area:**

Area of the quadrilateral PQRS = 1/2 × *d *× (*h*_{1}
+ *h*_{2}) sq. units

= 1/2 × 6 × (4.3 + 1.7) cm^{2}

= 3 × 6 cm^{2}

= 18 cm^{2}

Area of the quadrilateral PQRS = 18 cm^{2}

^{}

**4. MIND, MI =3.6 cm, ND = 4 cm, MD= 4 cm, **

**Solution:**

**Given:**

mi = 3.6 cm, ND = 4
cm, MD = 4 cm, ∠M = 50° and ∠D = 100°

**Steps:**

1. Drawn a line segment MI = 3.6 cm

2. At M on MI made an angle ∠IMX = 50°

3. Drawn an arc with center M and radius 4 cm let it cut MX it D

4. At D on DM made an angle ∠MDY = 100°

5. With I as center drawn an arc of radius 4 cm, let it cut DY
at N.

6. Joined DN and IN.

7. MIND is the required quadrilateral.

**Calculation of Area:**

Area of the quadrilateral MIND = 1/2 × *d* × (*h*_{1}
+ *h*_{2}) sq. units = 1/2 × 3.2 × (2.7 + 3.3) cm^{2}

= 1/2 × 3.2 × 6 cm^{2} = 9.6 cm^{2}

Area of the quadrilateral = 9.6 cm^{2}

^{ }

**5. AGRI, AG= 4.5 cm, GR = 3.8 cm, **

**Solution:**

AG = 4.5 cm, GR = 3.8 cm, ∠A = 90°, ∠G = 110°, ∠R = 90°

**Steps:**

**1.** Draw a line segment AG = 4.5 cm

**2.** At G on AG made ∠AGX =110°

**3.** With G as centre drawn an arc of
radius 3.8 cm let it cut GX at R.

**4.** At R on GR made ∠GRZ = 90°

**5.** At A on AG made ∠GAY = 60°

**6.** AY and RZ meet at I.

**7.** AGRI is the required quadrilateral.

**Calculation of Area:**

Area of the quadrilateral AGRI = 1/2 × *d* × (*h*_{1
}+ *h*_{2}) sq. units = 1/2 × 6.8 × (2.5 + 2.4) cm^{2}

= 1/2 × 6.8 × 4.9 cm^{2} = 3.4 × 4.9 cm^{2}

Area of the quadrilateral = 16.66 cm^{2}

**II. Construct the following trapeziums
with the given measures and also find their area.**

**1.
AIMS with ****̅****A****̅****I****̅ ****|| S****̅M****̅****, AI = 6
cm, IM = 5 cm, AM = 9 cm and MS = 6.5 cm.**

**Solution:**

Given AI = 6cm, IM = 5cm

AM = 9cm, and A̅I̅ || S̅M̅

MS = 6.5 cm

**Construction :**

**Steps: **

1. Draw a line segment AI = 6cm.

2. With A and I as centres, draw arcs of radii 9 cm and 5 cm
respectively and let them cut at M

3. Join AM and IM.

4. Draw MX parallel to AI

5. With M as centre, draw an arc of radius 6.5 cm cutting MX at
S.

6. Join AS AIMS is the required trapezium.

**Calculation of Area:**

Area of the trapezium AIMS = 1/2 × *h* × (*a + b*)
sq.units

= 1/2 × 4.6 × (6 + 6.5)

= 1/2 × 4.6 × 12.5

= 28.75 Sq.cm

** **

**2.
CUTE with C** **̅U || ****̅****E**̅**T****̅****, CU = 7 cm, ****∠****UCE = 80°, CE = 6 cm and
TE = 5 cm.**

**Solution: **

Given : In the trapezium CUTE,

CU = 7cm, ∠UCE = 80°,

CE = 6 cm, TE = 5cm and C̅U̅ || E̅T̅

**Construction:**

**Steps:**

1. Draw a line segment CU = 7 cm.

2. Construct an angle ∠UCE = 80° at C

3. With C as centre, draw an arc 5 of radius 6 cm cutting CY at
E

4. Draw EX parallel to CU

5. With E as centre, draw an arc of radius 5 cm cutting EX at T

6. Join UT. CUTE is the required trapezium.

**Calculation of area:**

Area of the trapezium CUTE = 1/2 × *h* × (*a + b*)
sq.units

= 1/2 × 5.9 × (7 + 5) sq.units

= 35.4 sq.cm

** **

**3.
ARMY with A** **̅R || Y** **̅M, AR = 7 cm, RM = 6.5 cm ****∠****RAY = 100° and ****∠****ARM = 60°**

**Solution:**

**Given : **

In the trapezium ARMY

AR = 7 cm, RM = 6.5 cm,

∠RAY = 100° and ARM = 60°, A̅R̅ || Y̅M̅

**Construction:**

**Steps:**

1. Draw a line segment AR = 7 cm.

2. Construct an angle ∠RAX = 100° at A

3. Construct an angle ∠ARN = 60° at R

4. With R as centre, draw an arc of radius 6.5 cm cutting RN at
M

5. Draw MY parallel to AR

6. ARMY is the required trapezium.

**Calculation of area:**

Area of the trapezium ARMY = 1/2 × *h* × (*a + b*)
sq.units

= 1/2 × 5.6 × (7 + 4.8) sq.units

= 1/2 × 5.6 × 11.8

= 33.04 sq.cm

**4.
CITY with C** **̅I || Y****̅****̅T, CI = 7 cm, IT = 5.5 cm, TY =
4 cm and YC = 6 cm.**

**Solution:**

**Given :**

In the trapezium CITY,

CI = 7 cm, IT = 5.5 cm, TY = 4 cm

YC = 6 cm, and C̅I̅ || Y̅T̅

**Construction:**

**Steps:**

1. Draw a line segment CI = 7 cm.

2. Mark a point D on CI such that CD = 4 cm

3. With D and I as centres, draw arcs of radii 6 cm and 5.5 cm
respectively. Let them cut at T. join DT and IT.

4. With C as centre, draw an arc of radius 6 cm

5. Draw TY parallel to CI. Let the line cut the previous arc at Y.

6. Join CY. CITY is the required trapezium.

**Calculation of area:**

Area of the trapezium CITY = 1/2 × *h* × (*a + b*)
sq.units

= 1/2 × 5.5 × (7 + 4) sq.units

= 1/2 × 5.5 × 11

= 30.25 sq.cm** **

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8th Maths : Chapter 5 : Geometry : Exercise 5.4 (Construction of Quadrilaterals and Trapeziums) | Questions with Answers, Solution | Geometry | Chapter 5 | 8th Maths

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