Given that [ABC]=10, find [BCD]

https://latex.artofproblemsolving.com/c/6/f/c6f8c6e18c3cdd46393c7b9a40dc8c4fb01243f6.png

[ ABC] = (1/2)AB * Height

10 = (1/2)*6 * Height

10 = 3 * Height

10/3 = Height

So

[ BCD ] = (1/2)BD * Height

[BCD ] = (1/2)(10) (10/3)

[BCD ] = 5(10/3)

[ BCD ] = 50 / 3

Here's one more way to solve this :

Triangles under the same height have the same area ratio as the ratio of their bases

[ BCD] / [ABC] = 10 / 6

[ BCD ] = [ 10/6] [ ABC]

[BCD ] = [ 10/6] [ 10]

[BCD ] = [ 5/3 ] [ 10]

[BCD ] = 50 / 3