Find the area of a regular pentagon with apothem length of about 10.3 meters. Round to the nearest tenth if necessary.Options:77.3 units2386.3 units2154.5 units2772.5 units2

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 musing 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 /2area 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 ΔOADTotal area =10×[tex]\frac{(5.15)^2}{2tan(36)}[/tex]  = 182.525447428574