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# Construction of a Square

Let us now construct a square when (i) its side is given and (ii) its diagonal is given

Construction of a Square

Let us now construct a square when (i) its side is given and (ii) its diagonal is given

1. Construction of a square when its side is given

Example 5.40

Construct a square LAMP of side 4 cm. Also find its area.

Solution:

Given: side = 4 cm

Steps:

1. Draw a line segment LA = 4 cm.

2. At L, construct LX LA .

3. With L as centre, draw an arc of radius 4 cm and let it cut LX at P.

4. With A and P as centres, draw arcs of radius 4 cm each and let them cut at M.

5. Join AM and PM. LAMP is the required square.

Calculation of Area:

Area of square LAMP = a2 sq.units

= 4 × 4 =16 sq.cm

2. Construction of a square when its diagonal is given

Example 5.41

Construct a square RAMP of a diagonal 8 cm. Also find its area.

Solution:

Given: diagonal = 8 cm

Steps:

1. Draw a line segment RM = 8 cm.

2. Draw the perpendicular bisector XY to RM. Let it bisect RM at O.

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

4. Join RA, AM, MP and PR.

5. RAMP is the required square.

Calculation of Area:

Area of square RAMP = a2 sq.units

= 5.7 × 5.7 = 32.49 sq.cm

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