Let us construct a parallelogram with the given measurements
1. Two adjacent sides and one angle.
2. Two adjacent sides and one diagonal.
3. Two diagonals and one included angle.
4. One side, one diagonal and one angle.

**Construction
of a Parallelogram**

**Let us construct a parallelogram with
the given measurements**

1. Two adjacent
sides and one angle.

2. Two adjacent
sides and one diagonal.

3. Two diagonals
and one included angle.

4. One side,
one diagonal and one angle.

** **

__1. Constructing
a parallelogram when its two adjacent sides and one angle are given__

**Example 5.30**

Construct
a parallelogram BIRD with BI=6.5*cm*, IR=5*cm* and ∠*BIR* = 70º . Also find its area.

*Solution:*

**Given:**

BI=6.5*cm*, IR=5*cm* and ∠
*BIR* = 70º

**Steps:**

1. Draw a
line segment BI=6.5*cm*.

2. Make an
angle ∠ *BIX*
=
70º
at I on ̅*B**̅**I**̅*.

3. With I
as centre, draw an arc of radius 5*cm* cutting
IX at R.

4. With B
and R as centres, draw arcs of radii 5*cm*
and 6.5*cm* respectively. Let them cut at
D.

5. Join BD
and RD.

6. BIRD is
the required parallelogram.

**Calculation of Area:**

Area of the parallelogram BIRD = *bh* sq.units

= 6.5× 4.7 = 30.55 *sq*.*cm*

** **

__2. Constructing
a parallelogram when its two adjacent sides and one diagonal are given__

**Example 5.31**

Construct
a parallelogram CALF with CA=7*cm*, CF=6*cm* and AF=10*cm*. Also find its area.

*Solution:*

**Given:**

CA=7*cm*, CF=6*cm* and AF=10*cm*

**Steps:**

1. Draw a
line segment CA=7*cm*.

2. With C
and A as centres, draw arcs of radii 6*cm*
and 10*cm* respectively. Let them cut at
F.

3. Join CF
and AF.

4. With A
and F as centres, draw arcs of radii 6*cm*
and 7*cm* respectively. Let them cut at
L.

5. Join AL
and FL.

6. CALF is the required parallelogram.

**Calculation of Area:**

Area of the parallelogram CALF = *bh* sq.units

= 7×5.9 = 41.3 *sq*.*cm*

** **

__3. Constructing
a parallelogram when its two diagonals and one included angle are given__

**Example 5.32**

Construct
a parallelogram ∆UCK with DC=8*cm*, UK=6*cm* and ∠ *DOU*
=110º
. Also find its area.

*Solution:*

**Given:**

DC=8*cm*, UK=6*cm* and ∠
*DOU* =110º

**Steps:**

1. Draw a
line segment DC=8*cm*.

2. Mark O
the midpoint of *D**̅**C**̅*.

3. Draw a
line *X**̅**Y**̅* through O which makes
∠ *DOY*
=
110º
.

4. With O
as centre and 3*cm* as radius draw two arcs
on ̅*X**̅**Y**̅* on either sides of
*D**̅**C**̅* . Let the arcs
cut *O**̅**X**̅*at K and *O**̅**Y**̅*at U

5. Join *D**̅**U**̅*, *U**̅**C**̅*, *C**̅**K**̅*and *K**̅**D**̅*.

6. DUCK is
the required parallelogram.

**Calculation of Area:**

Area of the parallelogram DUCK = *bh* sq.units

= 5.8 × 3.9 = 22.62 *sq*.*cm*

** **

__4. Constructing
a parallelogram when its one side, one diagonal and one angle are given__

**Example 5.33**

Construct
a parallelogram BEAR with BE=7*cm*, BA=7.5*cm* and ∠ *BEA*
=
80º
. Also find its area.

*Solution:*

**Given:**

BE=7*cm*, BA=7.5*cm* and ∠
*BEA* = 80°

**Steps:**

1. Draw a
line segment BE=7*cm*.

2. Make an
angle ∠ *BEX*
=
80º
at E on *B**̅**E**̅*.

3. With B
as centre, draw an arc of radius 7.5*cm*
cutting EX at A and Join BA.

4. With B
as centre, draw an arc of radius equal to the length of *A**̅**E**̅*.

5. With A
as centre, draw an arc of radius 7*cm*.
Let both arcs cut at R.

6. Join BR
and AR.

7. BEAR is
the required parallelogram.

**Calculation of Area:**

Area of the parallelogram BEAR = *bh* sq.units

= 7×4.1 = 28.7 *sq*.*cm*

Tags : Questions with Answers, Solution | Geometry | Chapter 5 | 8th Maths , 8th Maths : Chapter 5 : Geometry

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8th Maths : Chapter 5 : Geometry : Construction of a Parallelogram | Questions with Answers, Solution | Geometry | Chapter 5 | 8th Maths

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