Find the area of the quadrilateral giving the answer to the nearest square unit.
The first thing we note is that in the figure each square represents one square unit. One way to find the area is to count the number of square units covered by the shape. We can estimate that this block is about one square unit, and so is this space. I also notice, if I combine these two spaces, they would probably be equal to one square unit. And if we combine these spaces, we would probably have an additional one square unit. Again, combining these two pieces would probably be the equivalent of one square unit, as with these two.
Now, let’s count how many square units we think we have. One, two, three, four. As we’re marking these off, we might notice two other small pieces in the shape. We’re able to combine the spaces with the other partial squares we found for the fifth and sixth square unit. A good estimate for the area here would be six square units.
There’s actually a way for us to be more accurate here. We find the area of a parallelogram by multiplying the base times the height where the height is the perpendicular distance from one base to the other. In this parallelogram, we can let this be one of the bases. So we say that the base of this parallelogram has a measure of two units. We’ll label the other base. And the height of this parallelogram will be the distance from one base to the other such that the intersection here is 90 degrees. This will represent the height of our parallelogram.
And when we count the squares, it’s a distance of three units. If the area is equal to the base times the height, then the area of our parallelogram will be equal to two units times three units, six square units. And this confirms our estimate. The area of this parallelogram is six square units.