Perimeter: Real-World Geometry Problems

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  • 0:01 Perimeter Review
  • 1:05 Problem 1: Brownies
  • 3:16 Problem 2: Garden Borders
  • 5:33 Lesson Summary
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Lesson Transcript
Instructor: Elizabeth Foster

Elizabeth has been involved with tutoring since high school and has a B.A. in Classics.

Watch this lesson to get some practice using perimeter in real-world situations. If you like baking brownies, you'll be able to use the math here to make your creations even more delicious!

Perimeter Review

In this lesson, we'll go over some problems that use perimeter in real-life situations, but first we'll quickly review what perimeter is.

The perimeter of a shape is the distance around the edge of the shape. For example, say you have a rectangle 10 feet long and 8 feet wide. The perimeter would be the length of all the sides added together:

10 + 10 + 8 + 8 = 36 feet

The same goes for a triangle: just add all the sides together to get the perimeter.

The perimeter of a circle is also called the circumference. You calculate the circumference with the formula

2 * pi * r

where r represents the radius of the circle. If you just have half of a circle, you can cut the value in half to get pi * r for the circumference.

To find the perimeter of a complicated shape, just break it down into combinations of lines, rectangles, circles, semicircles, and triangles.

Problem 1: Brownies

Now that we've reviewed perimeter, we'll look at some real-life problem examples. First, we're going to take a look at a very important brownie dilemma.

Josh is baking brownies. His brownie batter could fit into one of three pans:

  • One 8 inch by 6 inch pan
  • One 12 inch by 4 inch pan
  • One 9 inch by 5 1/3 inch pan

All of the pans are 2 inches deep. Josh wants to get the greatest possible amount of crispy edge on his brownies; he doesn't like the middle pieces, but he loves the edge pieces with a little more crunch to them. Which pan should he use?

This is a question about perimeter. The pieces with crispy edges are the pieces around the outside of the pan, so to maximize the crispy edge, Josh needs the pan with the biggest perimeter.

You'll notice that all of the pans can hold exactly the same amount of brownie batter. For each pan, the total area of the bottom of the pan is 48 square inches, and the depth is 2 inches, so each pan can hold a total of 96 cubic inches of batter. You might think that because of this, the perimeters would all be the same. But you'd be wrong! Let's add up the perimeter of each of these different pans:

Pan 1: 8 + 8 + 6 + 6 = 28
Pan 2: 12 + 12 + 4 + 4 = 32
Pan 3: 9 + 9 + 5 1/3 + 5 1/3 = 28 2/3

The perimeter of pan 2 is bigger than the others, so if Josh wants the maximum amount of crispy brownie edges, he should go with Pan 2.

On the other hand, let's say you disagree with Josh and you're a fan of the middle pieces. That means you'd want to minimize the outside edges to get the maximum possible of the gooey, melty, middle-of-the-pan brownies. You could get really sneaky and sabotage Josh by giving him Pan 1 instead!

Problem 2: Garden Borders

Fortified by a delicious pan of brownies, it's time to turn to some home improvement.

Lucy is putting a fence around her garden. Her garden looks like this. If fencing costs $2.50 per foot, how much will Lucy pay to fence her garden?

garden perimeter

Once again, you can see that this is a perimeter problem: to find out how much fencing Lucy needs, we need to find the perimeter of the garden. This time, it's not quite as easy to find the perimeter though, because we have a rectangle with rounded edges.

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