LESSON PROBLEM: Area: If you have to find the area of a region, which is not a regular shape, how would you calculate it?

STUDY GUIDE

Rice farmers need to know the area of each of their paddy fields. They use measurement skills and geometry to help them. Let's define the concept of area. Area measures the surface, or enclosed space of an object.  The two figures below represent rice seedling trays. Can you tell, which one occupies more space, or which is bigger?

 1 2 3 4 5 6 7 8 2 3 4

 1 2 3 4 5 2 3 4 5

In order to find the area of a surface, we can use a grid. To measure the area in the figures above, we need a centimeter grid.  A centimeter grid means a graph, which is made up of squares. Each square is one centimeter long and one centimeter wide. We can count the squares and find the area of the figures in square centimeters.

In the first figure which is a rectangular tray, the length is 8 units and the width is 4 units. We have four rows of 8 squares in each row.  The total number of squares in the first figure equals 32.  If each square is a centimeter square, then the total area of the rectangle is 32 square centimeters. We can solve this by adding all of the squares, or by multiplying the number of squares in each row, with the number of squares in each column.
4 x 8 = 32

The second figure representing the second seedling tray is 5 units long and 5 units wide.  It is a square.  The total number of squares in this figure is 25, 5 rows of 5 squares each.  5 x 5 = 25 So the total area of this square is 25 square centimeters.

Whatever the shape of the surface of the plane, its area is measured in square units.  When it is a small surface, like rice seedling trays, we measure it in square centimeters (or in square inches). If it is a bigger surface, say the floor of a store room for rice, we measure it in square feet. If it is a rice field, we measure it in square meters or yards. If it is a city or village, we measure it in square kilometers or miles.

Area is measured in square units.

But it is not necessary to draw squares on all of these surfaces. We can just multiply the two dimensions of the surface.

Length x Width = Area

This is what we did in the examples above.  To find the area of the rectangle, you added 8 + 8 + 8 + 8 - four rows of eight squares each.  You know that the repeated addition of a number is the same as multiplying the two numbers.  Rather than add 8 four times, we easily multiply it by 4, and arrive at the answer.  8 x 4 = 32.

Similarly, in the second figure, which is a square tray we multiplied 5 by 5 and got the area of the square. 5 x 5 = 25

Now you find the area of the following surfaces for which length and width is given:

1. length = 9 cm;  width = 6 cm
2. length  = 7 cm; width = 4 cm
3. length  = 9 meters; width = 7 meters
4. length = 25 meters; width = 20 meters
5. length = 80 meters;  width = 60 meters
6. length  = 15 meters; width = 12 meters
7. length  10 meters; width = 10 meters
8. length = 11 meters;  width = 11 meters
9. length  = 45 meters; width = 20 meters
10. length  = 50 kilometers; width = 35 kilometers

Now take a look at this irregular figure representing an Arkansas rice farm. It is in pink, blue and green.  Use the method we learned above to calculate the area of the three different rice fields.  Just count the squares, and you get the area .

We have 2 x 4 = 8 green squares, 2 x 3 = 6 blue squares, and 2 x 6 = 12 pink squares.

Let's add these up to get the total area of planted rice on the rice farm. 8 + 6 + 12 = 26.  The area of the planted fields of the farm is 26 square units. Or if we know that each square represents one square meter, then the area is 26 square meters.

In mathematics, we use symbols as much as possible.  Let's write square meters as m2.  So 26 square meters shall be written as 26 m2.

Now find the area of the sections of the following larger rice farm. Write your answers using the correct symbols. Each square represents a square meter. The purple and yellow planes represent seedling nurseries. What is the area of the seedling nurseries together? The green and blue planes are the two large rice paddies of the farm. What is the area of each? What is the area when they are combined? This Arkansas rice farm has a small rice mill within it. It is represented by the red squares. What is the area of the mill?

It is useful to know that 10,000 m2 is measured as one hectare. Most farms and fields around the world are measured in hectares. In the United States they are measured in acres. So you can imagine how big these are.

ACTIVITIES

Take some graph paper and draw a layout of a rice farm. The shapes you draw should include small and big squares, small and big rectangles, small and big irregular polygons. Label the different buildings and fields. Calculate the areas of the different sections of your farm.

EXTENDED LEARNING

Draw a circle, an oval shape and a triangle on a graph paper. Try to calculate the area of all these figures.

Draw a 10cm x 6cm rectangle. Draw a 1 cm border inside its boundary. Calculate the area of the surrounding border (road) and the area left inside.

You can get some help at this site.
http://www.math.com/school/subject3/lessons/S3U2L4DP.html

VOCABULARY
• dimension
• irregular
• surface
• rectangle
• polygons