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ICSE Class 10 Answered

How to draw a regular pentagon given the measure of its 1 side using ruler and compass only?
Asked by nehalrvora | 14 Feb, 2019, 09:35: AM
answered-by-expert Expert Answer
First let us draw a plan figure for a regular pentagon PQRST as shown in figure. Let us assume its sides are 5 cm.
We know for a regular pentagon each interior angle is 108°. In order to draw the regular pentagon only with ruler and compass,
let us calculate the length of sode QT of triangle PQT. since begin mathsize 12px style angle end stylePQT=begin mathsize 12px style angle end stylePTQ = 36º, we have QT = 2×5×cos36  = 8.1 cm .
Similarly side PR also equal to 8.1 cm
 
Let us assume the given measure of one side AB of regular pentagon is 5 cm.   
Using  A as centre, let us draw an arc of radius 8.1 cm . Similarly using B as centre let us draw
an arc of radius 5 cm. Let both the arc meet at D. 
 
Similarly using A as center draw an arc of radius 5 cm and using B as centre, draw an arc of radius 8.1 cm.
Let these arcs meet at C. Let us join AC and BD.

Now using C as centre, draw an arc of radius 5 cm and using D as centre, draw another arc of radius 5 cm.
Let these arcs meet at E. Join CE and DE
 
Now ABDEC is the regular pentagon of sides 5 cm.
 
 
Answered by Thiyagarajan K | 14 Feb, 2019, 12:01: PM

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