jimmylow wrote:

16. The triangles in the figure above are equilateral and the ratio of the length of a side of the larger triangle to the length of a side of the smaller triangle is 2/1. If the area of the larger triangular region is K, what is the area of the shaded region in terms of K?

(A) 3/4K

(B) 2/3K

(C) 1/2K

(D) 1/3K

(E) 1/4K

A would be my answer.

Area of shaded = Area of Large - Area of Small

Give: Area of Large = K

We need to find Area of Small in term of K.

Triangle area = 1/2 * base * height

and since a side of the large triangle is twice larger than a side of small triangle, we are dealing with (1/2) * (1/2) = 1/4 factor.

Therefore, Area of shaded = K - K/4 = 3K/4