# To construct a regular pentagon of given sides using tape.

• Author: Farhan Khan
• Posted On: April 24, 2021
• Updated On: April 24, 2021

## 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 ∟leB= 108 º,

We know that, ∟leA + ∟le B +∟le C = 180 º

leA +∟le C = 180 º – 108 º

leA = ∟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:

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

### ii) Method -2:

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

### iii) Method -3:

1. Select a chain line on the ground.
2. Mark points A & B at a distance of 5 m from A.
3. Erect perpendicular at B by 3-4-5 method and mark a point B’ at a distance of 5m on that perpendicular line.
4. Bisect AB to get point 1 on AB.Extend the bisection line to a convenient distance and mark point 2.
5. Join A & B’ to get point 4.
6. B as centre,BA as radius cut an arc on line 1-2 to get 5
7. Measure the distance between 4 and 5 and bisect it to get point 6.
8. B as centre BA as radius draw an arc.
9. 6 as centre 6B as radius cut an arc to get point C.
10. Repeat the same procedure at point A to get point E.
11. After getting E and C, E as centre and ED =5m as radius cut the arc and repeat the same from C.

## Result:

Author: Farhan Khan

Farhan is a highly experienced civil engineer from the Southern side of Texas and has been associated with ConstructionHow since 2020. Over almost a decade, his wide span of expertise enabled him to bring forth his fair share of stories and experiences related to the most iconic engineering examples worldwide. He has also contributed to online and offline publications on requests. Engineering is his passion, which is why he chose to become part of our honorable team of industry experts looking to provide authentic and credible guidelines to the reader.