Table of Contents

## Construction Of A Regular Pentagon

## Aim:

To construct a regular pentagon of given sides using tape or chain and other accessories.

## Instruments Required:

Chain, Tape, Arrows, Ranging Rods, Cross staff etc.

## Theory:

Using tape and chain any regular figure can be constructed .The included angle of the given regular figure can be calculated as below. The included angle of the regular pentagon is determined as follows.

Included angle Ө = __(2n-4)/n__ 90 º

Where,

n = number of sides

Ө = included angle

There fore here

n=6

Ө = __(2 x 5-4)/6__ x 90 º

Ө =108 º |

### Calculations:

In. triangle ABC, if ∟^{le}B= 108 º,

We know that, ∟^{le}A + ∟^{le }B +∟^{le }C = 180 º

∟^{le}A +∟^{le }C = 180 º – 108 º

∟^{le}A = ∟^{le }C =36 º

By sin rule,

__AC /Sin B__ = __AB/ Sin C__

AC= __AB x Sin B/ Sin C__

AC= __5 x Sin 108__ º/ Sin 36 º

There fore AC = 8.09 m =8.10 m

## Procedure:

### i) Method -1:

- Select a chain line on the ground
- Mark points A & B at a distance of 5 m from A.
- To get point C, keep B as centre 5m as radius (Regular pentagon) cut an arc.
- Keep A as centre, 8.10 m as radius cut the arc which is drawn in step 3, to get point C.
- Repeat the same procedure to get E from A & B.
- To get point D take 5m from E and C, bisect to get point D.

### ii) Method -2:

- Select a chain line on the ground
- Mark points A & B at a distance of 5 m from A.
- Erect perpendicular at B by 3-4-5 method and mark a point B’ at a distance of 5m on that perpendicular line.
- Bisect AB to get point 1 on AB.
- A as centre AB’ as radius draw an arc to cut chain line at the point 2.
- With B as centre draw an arc of 5 m.
- With A as centre and A2 as radius draw an arc to cut the previous arc at C.Join B & C

### iii) Method -3:

- Select a chain line on the ground.
- Mark points A & B at a distance of 5 m from A.
- Erect perpendicular at B by 3-4-5 method and mark a point B’ at a distance of 5m on that perpendicular line.
- Bisect AB to get point 1 on AB.Extend the bisection line to a convenient distance and mark point 2.
- Join A & B’ to get point 4.
- B as centre,BA as radius cut an arc on line 1-2 to get 5
- Measure the distance between 4 and 5 and bisect it to get point 6.
- B as centre BA as radius draw an arc.
- 6 as centre 6B as radius cut an arc to get point C.
- Repeat the same procedure at point A to get point E.
- After getting E and C, E as centre and ED =5m as radius cut the arc and repeat the same from C.