mattnyc15 wrote:
OA:
24
Why wouldn't you add the additional triangle length to the area of 21.
When I solve for x: 3x(3)=21, I get 2.3
and when I plug that in for the triangle:
I get an area of 3.45 and add it to 21 for 24.45. It's close, but it's not the answer here.
The problem is that though side EC = 3x, side AB = 4x, so it isn't true that 3x * 3 = 21. (Side DC = x + 3x = 4x. Opposite sides of a parallelogram are equal, so DC = AB = 4x.)
So the shape ABCE is a trapezoid. Area of trapezoid = Height* (Base 1 + Base 2)/2
Base 1 = EC = 3x
Base 2 = AB = 4x
Height = 3
Area = 3* (3x + 4x)/2; we're told that this is 21
3* (3x + 4x)/2 = 21
Solving, we get x = 2.
So Base of parallelogram = 4x = 4*2 = 8
Height = 3
Base * Height = 8*3 = 24
(Or, thinking of it as you did, if x = 2, the area of the triangle would be (2*3)/2 = 3. 21 + 3 = 24.)
