Question

draw a regular pentagon and then a triangle of the same area. calculate the area

Answer 1

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

 

 

Answer 2

Answer:

check this pic

Step-by-step explanation:

calculate the area-

∆FDG is the required triangle

Area of pentagon ABCDE = Area of ∆ FDG

= 1/2 ×9×6

= 27cm²

hope it helps