Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Regular Polygon Area GEOMETRY NAME_________________________ DATE __________ Per.___________ 1 Here is a method for finding the area of a regular polygon using the formula: A = ap Find the area of this regular trigon (n = 3), 2 also known as “triangle”. a) To find the interior angle sum use the formula: Area & Perimeter 180(n − 2) = 180(3 − 2) = 180 interior angle radius s apothem a r b) To find the interior angle measure divide by n: 180(n − 2) 180(3 − 2) 180 = = = 60 n 3 3 c) To find the base angle measure divide by 2: 60 ÷ 2 = 30 opp d) To find the apothem a, use trigonometry: sin = a hyp sin30° = ⇒ a = r sin30° r a r For r = 10, a = 10 ⋅sin30° = 10( 0.5) = 5 30° adj x cos = cos30° = ⇒ x = r cos30° hyp r For r = 10, x = 10 ⋅ cos30° = 10(0.866 ) = 8.66 e) To find the adjacent side x: x base angle r x 30° f) To find the polygon side s, multiply the ∆ adjacent side by 2. s = 2x = 2r cos30° = 2(10cos30°) = 2(8.66 ) = 17.321 g) To find the perimeter p, multiply the polygon side by n: p = ns = 3(17.321) = 51.962 h) To find the area, substitute the apothem a and the perimeter p, into the formula: 1 1 ap = (5)(51.962) = 129.905 2 2 1. Pentagon radius = 10 n= 5 Interior ∠ Sum = 180(n–2) = 180(5–2) = ∠ Measure = 180(5–2)/5 = 540 ÷ 5 = Base ∠ = 180(n–2)/n ÷ 2 = 108 ÷ 2 = Apothem = r sin 54°=10 sin 54° = Right ∆ Base = r cos 54° = 10 cos 54° = PolySide = 2rcos 54° = 20 cos 54° = Perimeter = n 2rcos 54° = 5(20) cos 54° = Polygonal Area = ap÷2 = n= 2. Hexagon radius = 10 Interior ∠ Sum = 180(n–2) = ∠ Measure = 180(n–2)/ n = Base ∠ = 180(n–2)/ n ÷ 2 = Apothem = rsin base∠ = Right ∆ Base = r cos base∠ = PolySide = 2rcos base∠ = Perimeter = 2rn sin base∠ = Polygonal Area = ap÷2 =