Let us now construct a rhombus with the given measurements
(i) One side and one diagonal
(ii) One side and one angle
(iii) Two diagonals
(iv) One diagonal and one angle

**Construction
of a Rhombus**

**Let us now construct a rhombus with the
given measurements**

(i) One side
and one diagonal

(ii) One
side and one angle

(iii) Two
diagonals

(iv) One
diagonal and one angle

** **

__1. Construction
of a rhombus when one side and one diagonal are given____ __

**Example 5.34**

Construct
a rhombus ROSE with RO = 5 *cm* and RS =
8 *cm*. Also find its area.

*Solution:*

**Given: **RO = 5 *cm* and RS = 8 *cm*

**Steps:**

1. Draw a
line segment RO = 5 *cm*.

2. With R
and O as centres, draw arcs of radii 8 *cm*
and 5 *cm* respectively and let them cut
at S.

3. Join RS
and OS.

4. With R
and S as centres, draw arcs of radius 5 *cm*
each and let them cut at E.

5. Join RE
and SE.

6. ROSE is the required rhombus.

**Calculation of Area: **

Area of rhombus ROSE = ½ × d_{1} × d_{2} sq.units

= 1/2 × 8 × 6 = 24sq.*cm*

** **

__2. Construction
of a rhombus when one side and one angle are given__

**Example 5.35**

Construct
a rhombus LEAF with LE = 6 *cm* and ∠ *L*
=
65º
. Also find its area.

*Solution:*

**Given: **LE = 6 *cm* and** **∠** ***L*** **=** **65º

**Steps:**

1. Draw a
line segment LE = 6 *cm*.

2. At L on
LE, make ∠ *ELX* = 65º .

3. With L
as centre draw an arc of radius 6 *cm*.
Let it cut LX at F.

4. With E
and F as centres, draw arcs of radius 6 *cm*
each and let them cut at A.

5. Join EA
and AF.

6. LEAF is
the required rhombus.

**Calculation of Area:**

Area of rhombus LEAF = 1/2 × d_{1} × d_{2} sq.units

= 1/2 × 6.4 × 10.2 = 32.64 sq.*cm*

** **

__3. Construction
of a rhombus when two diagonals are given__

**Example 5.36**

Construct
a rhombus NEST with NS = 9 *cm* and ET =
8 *cm*. Also find its area.

*Solution:*

**Given:** NS = 9 *cm* and ET = 8 *cm*

**Steps:**

1. Draw a
line segment NS = 9 *cm*.

2. Draw the
perpendicular bisector XY to NS. Let it cut NS at O.

3. With O
as centre, draw arcs of radius 4 *cm* on
either side of O which cut OX at T and OY at E.

4. Join NE,
ES, ST and TN.

5. NEST is
the required rhombus.

**Calculation of Area: **

Area of rhombus NEST = ½ × d_{1} × d_{2} sq.units

= 1/2 × 9 × 8 = 36 sq.*cm*

__4. Construction
of a rhombus when one diagonal and one angle are given__

**Example 5.37**

Construct
a rhombus FARM with FR = 7 *cm* and ∠* F *=* *80º* *. Also find its area.

*Solution:*

**Given: **FR = 7 *cm* and** **∠** ***F*** **=** **80º

**Steps:**

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

2. At F,
make ∠ *RFX*
=
∠ *RFY*
=
40º
on either side of FR.

3. At R,
make ∠ *FRP*
=
∠ *FRQ*
=
40º
on either side of FR.

4. Let FX
and RP cut at M and FY and RQ cut at A.

5. FARM is
the required rhombus.

**Calculation of Area: **

Area of rhombus FARM = ½ ×
*d*_{1} × *d*_{2} *sq.units*

= ½ × 7 × 5.9 = 20.65*sq.cm*

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

Study Material, Lecturing Notes, Assignment, Reference, Wiki description explanation, brief detail

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

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