Area of Polygons Questions and Answers - Form 2 Topical Mathematics

Questions

1. Find the area of a regular polygon of length 10 cm and side n, given that the sum of interior angles of n : n –1 is in the ratio 4 : 3
2. Calculate the area of the quadrilateral ABCD shown:-
   
   

Answers

1. 180( n – 2)     =  4
   180 (n -1 – 2)     3
   540n – 1080 = 720n – 2160
   720n – 540n – 2160 – 1080
   180n = 1080
   n = 6
   Area of hexagon = 6 (½ x 10 x sin 60)
   = 6 x 43.30 = 259.81 cm²
2.  
   
   Area ∠rt Δ = ½ x 8 x 6
   S = ^{(12 + 14 + 10)}/₂
   A = √[18(18-12) (18-14) (18-10)]
   = √(18 x6 x 4 x 8)
   = √3456
   = 58. 79
   Total area = 24 + 58.79 = 82.79