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Perimeter of Quadrilaterals and Irregular or Combined Shapes

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  • 0:09 Finding the Perimeter
  • 0:40 Quadrilaterals
  • 2:22 Irregular Shapes
  • 3:07 Combined Shapes
  • 5:44 Lesson Summary
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Lesson Transcript
Instructor: Jeff Calareso

Jeff teaches high school English, math and other subjects. He has a master's degree in writing and literature.

Sometimes you need to figure out a shape's perimeter whether you have all the information you want or not. In this lesson, you'll learn how to find the perimeter of any quadrilateral as well as more complicated irregular and combined shapes.

Finding the Perimeter

Let's say you like running. Normally, you run on a track. You know the track is 400 meters long. If you think about it, that 400 meters is the perimeter of the oval. Perimeter, as you'll recall, is the path around the outside of a shape.

But, what if you get tired of running in endless ovals? Maybe you'd rather run around the block where you live. Or, maybe you want to wind a bit through your neighborhood. How do you know how far you went? There's where knowing how to find a perimeter is essential.

Quadrilaterals

Let's start with you running around your block and wanting to know the distance, or perimeter. If you look at your block on a map, it has four sides. That makes it a quadrilateral. A quadrilateral is just a four-sided shape. If you're lucky, you know how long each side is.

North Street and South Street are each 250 meters long. East and West Streets are each 100 meters long. To find the perimeter of this block, just add up the sides. That's 250 + 250 + 100 + 100 = 700 meters. That's almost two times the length of the track, and you're already home when you're done!

But, what if you don't know how long each street is? Let's say you're staying at your cousin's house and want to run in that neighborhood. She tells you that she knows George Street is 100 meters and John Street is 50 meters. What about Paul and Ringo? Fortunately, you recognize that the corners on this block are right angles. Therefore, this is no ordinary quadrilateral; it's a rectangle. And, you know that the opposite sides of rectangles are congruent, or equal in length. So, if George Street is 100 meters, then so is Ringo Street. If John Street is 50 meters, so is Paul Street. Therefore, the perimeter of this quadrilateral, and the distance you ran, is 100 + 100 + 50 + 50, or 300 meters. That's a small block, less than one lap around the track.

If you know the length of all four sides of a quadrilateral, you can always find the perimeter by just adding them. If a side or two is missing, see if you can figure out the missing information using your knowledge of the shape's properties. Remember, with squares and rhombuses, all four sides are equal, so you only need to have one side given. With squares and parallelograms, the opposite sides are equal.

Irregular Shapes

But, what happens when you get so good at running that you're ready to train for a marathon? That's 26.2 miles. You'll need to run a much bigger loop while you train, and it may not be such a tidy rectangle. It might look more like this:

Example of an irregular shape
example of an irregular shape

If you need to know the perimeter of an irregular shape like this, then you really do need to know the lengths of each side.

Fortunately, you spotted helpful signs along your way, and you noted how many miles each street was. To find the perimeter, just add up each length. In miles, this example is 6 + 2 + 3 + 4 + 4 + 4 + 3, or 26 miles. That's almost a full marathon! If you add in that .2 mile-long detour you took to flag down an ice cream truck at the end, you just ran a marathon distance!

Combined Shapes

The next time you go for a long training run, the route doesn't have helpful signs to tell you how long each street is. If that's the case, you may be able to figure out the perimeter by treating your route as a group of combined shapes. Let's look at this example:

Example of combined shapes
example of a combined shape

We know the lengths of some of the sides, but not all of them. But, look closer at the shape. It's actually a combined shape comprised of a group of squares and rectangles.

In the top square, we know two sides are 4 miles, so the other side must also be 4 miles. As for the bit below it, well, we know the entire length of that rectangle is 10 miles. If two sections are 3 and 4, then the missing part must be 3 miles.

And, on the part on the side, the small length is going to be equal to the opposite side of the small rectangle, so it's 1 mile. Finally, the remaining part is just 5 minus 2, or 3 miles. So, now we know all the sides! It's 4 + 4 + 4 + 3 + 1 + 2 + 1 + 3 + 10 + 5 + 3, or 40 miles. Holy cow! That's way farther than you planned. I think you earned some ice cream.

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