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
+128 
