A rectangle is made out of unit squares as shown below. Find the total area in square units of the red shaded region.
The area of the whole figure = 7 * 5 = 35 units^2
The white triangle has a base of 2 and a height of 5
So....its area = (1/2) (2)(5) = (1/2)10 = 5 units^2
So....the area of the shaded red part = 35 - 5 = 30 units^2
You could've done it using CPhill's way, but another way is to find the area of the rectangle and subtract it by the area of the red shaded region.
The top right-hand side triangle has dimensions of 6 by 5. This means the area is 15 units.
The far left-handed side rectangle has dimensions of 1 by 5. This means the area is 5 units.
The last triangle has dimensions of 4 by 5. This means the area is 10 units.
Now we can add them up to get 30 square units.
What CPhill did was use COMPLEMENTARY COUNTING which means finding the opposite of what you are supposed to find.
We were supposed to find the area of the red shaded region, but instead found the area of the white region and subtracted it from the whole rectangle.
This way is faster than what I did. This makes this "trick" very useful in math.
So just remember about the strategy and it might help you later in life.
P.S: I sound like a professor conducting a speech. Sorry to sound so formal!