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7th Grade Math / Lesson 1: Basic Shapes

What will we be learning in this lesson?

  • In this lesson you will review finding perimeter, circumference and area 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

Perimeter and Circumference

  • Perimeter and Circumference refer to the same part of shapes. When you talk about perimeter or circumference, you are talking about the distance around the outside of the shape. We use the word circumference when we want the distance around the outside of a circle. We use the word perimeter for the distance around any other 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. It is a little more difficult finding the circumference.

Perimeter and Circumference

  • 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.

Perimeter and Circumference

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.

Perimeter and Circumference

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)

Perimeter and Circumference

Here is a circle. A circle has a formula to follow to find its circumference. Let's first look at the parts of a circle.

The distance around the outside of the circle we said was the circumference. We also have a line that runs directly through the middle of the circle. This line is called the diameter. If you take half of this line, from the center of the circle to the edge of the circle is called the radius.

Perimeter and Circumference

The formula to find the circumference of a circle is C = p * d.
C stands for circumference , d stands for diameter, and p (called "pie") is a value used with circles. It is equal to 22/7 which is rounded to 3.14. We will use 3.14 for our calculations.

If the diameter of the circle below is 5 inches, find the circumference.

C =p * d
Use 3.14 for p and 5 for d (diameter).
C = 3.14 * 5
= 15.7
The circumference is 15.7 inches


  • 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.

    6 * 4 = 24                                                                                 3 * 3 = 9
    Area equals 24 square inches                               Area equals 9 square inches

  • Areas

  • 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?

  • Areas

  • 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.

  • Areas

    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.

      ½ * base * height
      ½ * 7 * 4
      ½ * 28 = 14
    The area of the triangle is 14 square cm


  • Finding the area of a circle is similar to finding the circumference of a circle. You need a formula.

  • The formula for the area of a circle is A = p * r2
    A means area, r means radius, and p is the 3.14 that we used with circumference.

    Find the area of the circle below.

    Remember, we need radius not diameter.
    Radius is 3 because it is half of the diameter.
    A = 3.14 * 32
       = 3.14 * 9
       = 28.26
    The area of the circle is 28.26 square inches.

    • Can you find the area, perimeter or circumference of a shape?
    • Go back to the classroom to get to your homework and any other items you need to attend to.