CE level Maths(AS,GS)

(a) s=(1/2)(5+7+8)=10
A=√[10(10-5)(10-7)(10-8)]=√300=3√10
(b)(i) Consider triangle A1A2B2
area of triangle A1A2B2/area of triangle A1A2A3=1/3
Since the ratio of the height between triangle A1A2B2 and triangle A2B1B2 is 3:2
area of triangle A2B1B2/area of triangle A1A2B2=2/3
So area of triangle A2B1B2/area of triangle A1A2A3=2/9
(ii) The area of triangle B1B2B3/area of triangle A1A2A3=1-3(2/9) : 1=3/9 : 1=1:3
(c)(i) area of triangle B1B2B3=(1/3)(area of triangle A1A2A3)
=>area of triangle Z1Z2Z3=(1/3)^(25)(area of triangle A1A2A3)=(1/3)^(25)3√10=√10/3^24
(ii) First term = 3√10, ratio=1/3
So, the area of all triangles = 3√10/(1-1/3)=9√10/2