#1**+1 **

Assuming that these are similar figures...and that the side of the larger triangle with a length of 6 corresponds to the side of the smaller triangle with a length of 2

The scale factor of the larger triangle to the smaller is just the above ratio = 6/2 = 3/1

This is the linear scale factor for any dimension....all corresponding sides of the larger figure to the smaller wil have this ratio...also...the height of the larger triangle to the smaller wioll also have this ratio

Perimeter is a linear measure...so ...the ratio of the perimeters will just be the same ratio 3 : 1

The ratio of the areas will be the square of the scale factor = (3/1)^2 = 9/1 = 9 : 1

So...the area of the the blue triangle will be :

Area of the smaller triangle * (scale factor)^2 =

2 * (3/1)^2 =

2 * 9 =

18 ft^2

To see this last part a litle more clearly

Note that the area of the smaller triangle = (1/2) base * height = (1/2) b * h

But since each dimension of the larger triangle is 3 times that of the smaller...its area is

(1/2) ( 3* base of smaller triangle) ( 3 * height of smaller triangle) =

(1/2) (3 b) (3 h) = (1/2) 9 bh = 9 [ (1/2) bh ] = 9 times [ the area of the smaller triangle]

Does that make some sense ???

CPhill
Jun 29, 2018