Answer:
The area = 182.52 sq units.
Step-by-step explanation:
- Area of regular polygon can be found by splitting into smaller triangles.
- Each triangle has base as side of polygon and vertex as center of polygon.
now consider ΔOAB,
we know ∠AOB = [tex]\frac{360}{5}[/tex]° =72°
(this is due to symmetry)
as ∠AOD = (∠AOB)/2 = 36°
Now we know AD=AB/2 =[tex]\frac{10.3}{2}[/tex] =5.15 m
using trignometric relation tan(∠AOD) =[tex]\frac{AD}{OD}[/tex]
⇒OD = [tex]\frac{AD}{tan(36)}[/tex] = [tex]\frac{5.15}{tan(36)}[/tex]
AREA OF TRIANGLE = BASE × HEIGHT /2
area of ΔOAD = [tex]\frac{1}{2}[/tex] × 5.15 × [tex]\frac{5.15}{tan(36)}[/tex]
= [tex]\frac{(5.15)^2}{2tan(36)}[/tex]
As there are 10 such triangles like ΔOAD
Total area =10×[tex]\frac{(5.15)^2}{2tan(36)}[/tex]
= 182.525447428574
