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** = *a*^{2} *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** = *a*^{2} *sq*.*units*

= 5.7 × 5.7 = 32.49 *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 Square | Questions with Answers, Solution | Geometry | Chapter 5 | 8th Maths

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