All About Shapes
Triangles? They're ok, but you hear about them everywhere. Squares, too. What about the more unusual shapes? Those ones with the funny names and weird properties. Let's learn a bit about them.
Quadrilaterals
First up: the quadrilateral. It's a mouthful, I know. But, what do you see in that word? Quad-. Where have you seen that? Quadruplets? How many babies is that? It's four! Or, about three more than a normal person can handle. A quadrilateral is just a four-sided shape.
Squares and rectangles are quadrilaterals. So are more unusual shapes, like the boomerang below:
Squares, rectangles and boomerangs are all quadrilaterals.
What do we know about quadrilaterals? If they have four sides, they also have four vertices, or corners. And, while those vertices can be any angle, they need to add up to 360 degrees. Why? Think about a square. All the angles are 90 degrees.
90 times 4 is 360. Now, what about that boomerang?
If that first angle is 130 degrees and the two small corners are 20 degrees, when we make those last two lines meet, the angle has to be 190 degrees. 130 + 20 + 20 + 190 = 360. No matter how you change the angles, they always add up to 360.
The perimeter of any quadrilateral is just the sum of the four sides. In the quadrilateral below, the sides, in inches, are 4, 4, 5 and 2.
The perimeter of this quadrilateral is 15 inches.
Therefore, the perimeter is 4 + 4 + 5 + 2, or 15 inches.
Is every square a quadrilateral? They always have exactly four sides, so yes. But, is every quadrilateral a square? Well, no. Some are rectangles. And, some are other things, like parallelograms.
Parallelograms
Do you remember what parallel means? Two parallel lines are two lines that will never meet. They're like the lines painted on the sides of an endless straight road.
A parallelogram is a four-sided shape with opposite sides that are parallel. Because of the parallel lines, the opposites sides are equal in length.
There are some unique properties of the angles inside parallelograms. First, the opposite angles are equal. Also, the adjacent angles are supplementary, which means they add up to 180 degrees.
The perimeter of the parallelogram below, where the sides are 4, 4, 5 and 5, is 18.
Example of a parallelogram
When we have a specific type of quadrilateral like the one below, we can determine its area.
The area of a parallelogram is base times height.
The area of a parallelogram is the base times the height. So, in this example, where the base is 7 inches and the height is - whoa, wait, 4 is not the height! Remember, the height is the distance from the base to the top, so while that side is 4 inches, the height is actually 3 inches:
kkk
The area of this parallelogram is 21 square inches.
So, the area is 7 times 3, or 21 square inches.
This is the same area formula as with squares and rectangles. And, if you remember, squares and rectangles also have sets of parallel sides, so they're both parallelograms!