#1**+2 **

first, we can subtract the area of the white from the area of the square. The top left triangle is x by 2x so the area is x^2. The triangle on the right is 3x by 4x so the area is 6x^2 the area of the bottom triangle is 2x by 4x so the area of that is 4x^2. the area of the whole square is 4x*4x=16x^2 16x^2-11x^2=5x^2

MIRB16 Jun 9, 2018

#2**+2 **

Not that much cluster, neat information.

To find the area of the shaded triangle in the diagram, we have to subtract the area of the unshaded triangles from the area of the whole square.

First, we need to find the area of all triangles, then add them up to receive the total area.

1st unshaded triangle(biggest triangle)= We use our trusty formula \(\frac{1}{2}*b*h\) . Plugging the values in, we have:

\(\frac{1}{2}*3x*4x=6x^2\).

2nd unshaded triangles(medium sized)=\(\frac{1}{2}*4x*2x=4x^2\) . The 2x came from 4x/2, because M is the midpoint of the side.

3rd unshaded triangle(smallest triangle)=\(\frac{1}{2}*x*2x=x^2\)

Now, we can add all the values up: \(6x^2+4x^2+x^2=11x^2\)

But, we're not done yet! We have to subtract the unshaded area(already found) from the total area of the square.

The area of the total square is:\(4x*4x=16x^2\) , since 4x is the side.

Thus, the area of the shaded triangle is:\(16x^2-11x^2=\boxed{5x^2}\)

.tertre Jun 9, 2018