Question

how to draw a regular pentagon of side 6 cm and then a triangle of the same area ?​

Answer 1

Answer:

Step-by-step explanation:

Take a regular pentagon of side 4cm

 

Angle at centre = 360/5 = 72

 

Half the angle = 72/2 = 36

 

Tan 36 = 2/h (Where h =  apothem)

 

h = 2/Tan 36

 

  = 2.75

 

 

Area = (½ x 4 x 2.75) x 5

       = 27.53 cm2

 

A triangle of the same area:

 

Assume base of triangle = 4cm

 

Area =  1/2bh

 

27.53 = ½ x 4 x h

 

27.53 = 2h

 

h = 13.8 cm

calculate the area-

∆FDG is the required triangle

Area of pentagon ABCDE = Area of ∆ FDG

= 1/2 ×9×6

= 27cm²

 

Answer 2

1. At First Draw 6cm Line with Scale
2. then Take your compass and measure the line
3. draw 5 sides with compass
4. draw Any 2 diagonals from same Point of the polygon
5. then measure one diagonal and Draw a parallel line of the diagonal
6. then do Same with the other diagonal
7. at last where each of the diagonal's Parallel line and the base of the pentagon intersects mark the point
8. now join the 1st point from which you have drawn the diagonal , with the 2 intersects
9. now u have your triangle
10. if wanna calculate the area then
11. Tan 36 = 2/h (Where h = apothem) h = 2/Tan 36.
12. Tan 36 = 2/h (Where h = apothem) h = 2/Tan 36.= 2.75. Area = (½ x 4 x 2.75) x 5.
13. Tan 36 = 2/h (Where h = apothem) h = 2/Tan 36.= 2.75. Area = (½ x 4 x 2.75) x 5.= 27.53 cm2. A triangle of the same area: Assume base of triangle = 4cm.
14. Tan 36 = 2/h (Where h = apothem) h = 2/Tan 36.= 2.75. Area = (½ x 4 x 2.75) x 5.= 27.53 cm2. A triangle of the same area: Assume base of triangle = 4cm.Area = 1/2bh. 27.53 = ½ x 4 x h. 27.53 = 2h. h = 13.8 cm.