Question

The figures are similar. The area of one figure is given. Find the area of the other figure to the nearest whole number. The area of a regular octagon is 35 cm2. What is the area of a regular octagon with sides three times as large?

A) 315 cm2
B) 225 cm2
C) 175 cm2
D) 105 cm2

Thanks!

Answer 1

area of a regular octagon with side length = a is given by

area = 2(1+root2)a^2

here area1 is given as 35
so 35 = 2(1 + root2)a^2

when side is made three times as large it is = 3a, then
area2 = 2(1 + root2)(3a)^2 = 2(1 + root2)(9a^2)

area1 35 2(1 + root2)a^2
----- ==> ------ = --------------------
area2 area2 2(1 + root2)(9a^2)

35 a^2 1
------ = -------- = -----
area2 9a^2 9

cross multiplying

35 x 9 = area2 ==> 315 = area2

ans is A) 315 cm^2

Answer 2

Thank you so much, very helpful!

Answer 3

pls do click GOOD ANSWER button if u r happy with the ans and the explanation o( ;})

Answer 4

u r welcome :D