Finding Area and Volume

Area and perimeter are geometric measurements used to measure plane figures. Perimeter is the distance around a figure. Area is the number of square units needed to cover a plane figure.

Materials: inch ruler, 20 unit squares (1 inch by 1 inch), and a 4-inch by 5-inch rectangle for each group

Preparation: Cut out the unit squares and rectangles from posterboard. Distribute 1 ruler, 20 unit squares, and 1 rectangle to each group.

Prerequisite Skills and Concepts: Students should know how to use a ruler and have an understanding of basic geometric ideas, including plane figures, polygons, and solid figures.

• Say: Perimeter is the distance around a figure. Look at the rectangle. Suppose you wanted to put a ribbon border around the rectangle. How can you find out how much ribbon is needed? (Measure the distance around the rectangle.)

• Say: Use your ruler to measure the length and width of the rectangle.
  Have students record each measurement of the rectangle. You may want to walk around the room to make sure each group labels the length and width correctly.

• Ask: What are the dimensions of the rectangle? (4 inches by 5 inches) What are the measures of the remaining two sides? (4 inches and 5 inches) How do you know?
  Students should know that opposite sides of a rectangle are equal in length.

• Ask: Now that you know the length of each side, how can you find out how much ribbon is needed? (Add the lengths of the sides.)

• Say: Add the lengths of the sides. How much ribbon is needed? (18 inches) So the perimeter of this rectangle is eighteen inches. It is the distance around the figure.

• Say: You can also use a formula to find the perimeter of a rectangle. P (perimeter) = (2 x l) + (2 x w).
  Have students find the perimeter using the formula.

• Say: Area is another way to measure a figure. Area is the number of square units needed to cover a plane figure.

• Say: Look at the unit squares. Each square is 1 inch long and 1 inch wide. Place the unit squares on top of the rectangle.

• Ask: How many unit squares were placed along the side that measures 5 inches? (5) How many unit squares were placed along the side that measures 4 inches? (4) How many groups of 5 unit squares are there? (4) How many unit squares are needed to cover the figure? (20)

• Say: So the area of this rectangle is 20 square inches.

• Ask: How could you find the area of this rectangle if you didn't have unit squares?
  Guide students to see that they could multiply the length times the width to find the area.

• Say: The formula for finding the area of a rectangle is A (area) = l (length) x w (width).

  You may wish to repeat this lesson using a rectangle with different dimensions.