a. Identify the area formula of different figures related to square; and
b. Inductively derive the area formula of rectangle, parallelogram, triangle, and trapezoid
Consider a rectangle that measures 3 units on one side. If a similar rectangle that measures 4 units on another side is superimposed on the first rectangle, how many square units will be formed?
Area is the number of square units in a certain area. There are 12 square units cover the entire rectangle. We can count the number of squares in a certain area, but how about if we are measuring a wide space area? We grasped the definition of multiplication that it is a repeated addition.
Instead of counting the box one by one, we just get the number of units in the two sides which are 3 and 4 (length and width), then multiply. When the children have grasped the idea of area through this diagrammatic presentation, then the teacher can have them devise a way of getting the correct answer through manipulation of symbols 3 and 4.
When children are taught to use the formula L x W to calculate area, the teacher simply engages them in a mechanical routine. But why does one multiply is not answered. This is the kind of question that lingers in the minds of children when teachers persistently emphasize calculations rather than understanding the rationale behind such task.
AREA OF A SQUARE
The area formula of a square is b x h. Since the base and height base are equal the formula will be A=b^2 or A=s^2
AREA OF A RECTANGLE
Comparing the area formula of square and the rectangle, the base and height ( length and width) of square are equal. Since the base and height of rectangle is not equal, the formula of rectangle is A=b x h. The formula derived from the area formula of square.
AREA OF A PARALLELOGRAM
The first figure is a parallelogram, if we will fold and cute the small triangle and put it in to the other side, it will form a perfect rectangle. The area formula is now the same with the area formula of rectangle A = b x h. The area formula of parallelogram derived from the area formula of rectangle.
AREA OF A TRIANGLE
If we will divide the parallelogram into two equal parts horizontally, it is composed of two equal triangles. The area of the triangle is half of the area of the parallelogram. To derive the area formula of the triangle, we just get the area formula of the parallelogram and add one half.
AREA OF A TRAPEZOID
If we will divide the parallelogram into two equal parts vertically, it is composed of two equal trapezoids.
The area of the trapezoid is half of the area of the parallelogram. To derive the area formula of the triangle, we just get the area formula of the parallelogram and add one half. Since the two bases of a trapezoid is not equal (b1 and b2), we just add the bases them multiply to the height.
VIDEO TUTORIAL
EXERCISES:
Answer the following problems. Feel free to draw a sketch
to help you answer the question.
I.
1. A rectangle measures 25 cm by 10 cm. What is its area?
2. The length of a rectangle is 12 cm and the area is 96
cm². What is the width?
3. I need to buy a carpet for a room that measures 3 m by
2 m. How many square meters do I need?
4. A painting measures 40 cm by 35 cm. How many squared cm
does its surface cover?
5. One side of a square measures 15 cm. What is its area?
6. If the area of a rectangle is 60 cm² and its width is
6 cm. What is its length?
7. The area of a square is 81 cm². What is the length of
one of its sides?
18. A parallelogram has a base of 3 in and a height of 7
in. What is its area?
19. A triangular-shaped yard has a base of 25 meters and
a height of 12 meters. What is its area?
10. A trapezoid has bases of 9 in and 7 in and a height
of 5 in. What is its area?
II.
1. A large window has a length of 8 feet and a width of 6
feet. What is its area?
2. A trapezoid has bases of 7 centimeters and 5
centimeters and a height of 3 centimeters. What is its area?
3. A rectangular piece of paper has a width of 16” and an
area of 192 in. What is its length?
More about area of plane figures
http://www.youtube.com/watch?v=XtsJrk-43d8
Songs and activities of plane figures
