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7th Grade Math / Lesson 3: Perimeter, Area, Volume

What will we be learning in this lesson?

  • In this lesson you will review finding perimeter, area, and volume of certain shapes.

    Vocabulary words are found in this purple color throughout the lesson. Remember to put these in your notebook.


  • Many words in this lesson will be interchangeable (they can be replaced by other words). Here are some of them.

  • Length = base

  • width = height


  • When you talk about perimeter, you are talking about the distance around the outside of the shape.
  • In real life situations, if you were to walk around the outside of a field, you are walking the perimeter of that field. If you were going to put a fence up around a yard, you would need to know the perimeter of the yard to know how much fence to buy.
  • When finding the perimeter of a shape, you are just going to add the lengths of all of the sides together.


  • Let's find some perimeters of the following shapes.

    Here is a square. What is special about a square? All sides are the same length. So, if this square has a side with the length of 6 inches, find the perimeter.

    Each side is 6 inches since this is a square.
    There are 4 sides so we have 6 + 6 + 6 + 6 = 24.
    The perimeter is 24 inches.


  • Here is a rectangle. What is special about a rectangle? Opposite sides are the same length. So, if this rectangle has a length of 6 inches and a width of 3 inches, find the perimeter.
    Since opposite sides are the same length, there are two sides with a length of 6 inches and two sides with a length of 3 inches.
    We have 6 + 6 + 3 + 3 = 18 The perimeter is 18 inches.


  • Here is a triangle. A triangle only has three sides, but you find the perimeter the same way you find the perimeter of squares and rectangles, add the sides together. Find the perimeter of this triangle.
    The sides are labeled 7, 7, and 5.
    So we have 7 + 7 + 5 = 17. The perimeter is 17 cm (centimeters)


  • Area is the amount of space on the inside of the shape.
  • Squares and rectangles are the easiest. To find out the area inside of these shapes, just multiply the length of the shape by the width of the shape.


  • Triangles are a little more involved than rectangles and squares. We saw that the area of a rectangle or a square was length * width. We will use this when finding the area of a triangle.
  • Look at the rectangle below. What happens when you draw a line from one corner to the opposite corner?


  • You get two triangles.
  • So one rectangle gives you two triangles. If we take one of those triangles away, we are left with one triangle, or half of the rectangle. So the area of that triangle is half of the area of the original rectangle.

  • The area of the triangle in the last slide was half of the area of the rectangle that it came from. This is the case for all triangles. The are half of a rectangle. So the area of a triangle if half of the area of a rectangle.
  • The area of a rectangle is length * width.
  • The area of a triangle is half of this.     ½ * length * width
               Or you might see it as    ½ * base * height
Find the area of the triangle below.
The height of the triangle is 4 centimeters.

  • The volume of  an object is the space inside of the object.
  • Area and volume both refer to the space inside of an object. The difference is that area talks about the space inside of a flat shape. Like the following shapes:
  • To find the volume, the shape needs another dimension to it so that it is not a flat shape. Like these:
  • The volume is the amount of space inside of the shape/object.

  • To find the volume of a basic box-shaped object you need to find the area of one side of the box, this will be called the base. Then take that area and multiply it by the height of the object.
  • Take a look at this box.
The bottom of the box is a rectangle with
      side lengths of 4 and 2. So the area of the
      bottom (base) is 4 * 2 = 8.
The height of the box is 3 in. So take the
      area of the bottom and multiply by 3.
             8 * 3 = 24
The volume of this object is 24 cubic inches.

  • Find the volume of this object.
  • Follow what we did on the previous example. Take the dimensions of the bottom, 14 and 2, and multiply them together. 14 * 2 = 28. Now take the 28 and multiply by the height. 28 * 5 = 140. 
  • So the volume of this object is 140 cubic cm.

  • Can you find the perimeter, area, or volume of a shape?

  • Go back to the classroom to get to your homework and any other items you need to attend to.