Construction of a Rhombus

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 × d₁ × d₂ 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 × d₁ × d₂ 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 × d₁ × d₂ 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 × d₁ × d₂ sq.units

 = ½ × 7 × 5.9 = 20.65sq.cm