Rectangle Area
Rectangle Area
In order to understand the formula for the rectangle area, we have to explore the following structure. [br](ps.: this structure was modified from the one made by Jayrton Carvalho)
Analysis 1
Move the bar and look as the rectangle is filled. How many little squares can fit in the rectangle?
Analysis 2
Change the base (B) measure to 10 and the height (H) to 5. Move the bar and look as the rectangle is filled. [br]How many little squares can fit in the rectangle?
Analysis 3
What is the connection between the number of little squares (n) that fit in the rectangle with the height (H) and the base (B) of the rectangle? [br]
Analysis 4
In theory, the number of small squares that fit in the rectangle can be considered the area of the rectangle.[br]Thus, write an equation that represents the area of a rectangle of base B and height H. [br]
What if this little square was smaller?
AREA OF SQUARE
PLAY WITH THE SQUARE
DESIGN A SQUARE WITH 4 CENTIMETER SQUARE AREA
DESIGN A SQUARE WITH 9 CENTIMETER SQUARE AREA
DESIGN A SQUARE WITH 16 CENTIMETER SQUARE AREA
DESIGN A SQUARE WITH 64 CENTIMETER SQUARE AREA
Bourke High School - Area of a circle
This animation demonstrates the area of a circle is equivalent to the area of the corresponding rectangle having the side dimensions of [math]r[/math] and [math]2\pi r[/math]. Move the black dot from left to right to 'explode' the circle into a rectangle.[br][br]The animation should prompt you to recall or derive the formula for the area of a circle (if in doubt, move the hint black dot from left to right).
Animation for the area of a circle
Investigation:[br]1) Move the slider above the circle and describe what happens to the circle step by step.[br]2) Make a conjecture about the formula for the area of a circle and show how you develope this formula. (move the slider named hint to help you)