In this assignment we will begin to study area, starting with perhaps the most simple shape of all, the rectangle. We will also start investigating areas of triangles. The main objective of this assignment is to understand why the area of a rectangle is the length times the width.
On an index card draw a square with sides 1 inch by 1 inch. Cut out the square. The area of this square is 1 square inch, and is often written as 1 inch2 (or 1 in2), and often spoken as 1 inch squared. Next, draw several rectangles on inch dot paper. Determine their areas by breaking each rectangle into 1 inch by 1 inch squares. Counting how many squares fill the rectangle will tell you the area of the rectangle.
Explain, using what you did in the previous step, why the area of a rectangle is equal to the length times the width. One thing to think about in doing this is: what is the relationship between multiplication (of whole numbers) and repeated addition?
If you have a square that is 1 foot by 1 foot, its area is 1 square foot. If you were to measure with inches instead of feet, what would its area be? (Recall that 1 foot is equal to 12 inches.) What does this tell you about converting areas from square feet to square inches? To test your answer, determine how many square inches there are in a figure whose area is 3 1/3 square feet.
If you take a rectangle and draw a diagonal you produce two right triangles. What is the relationship between these triangles (e.g., do they have the same shape)? Determine, in terms of the length and the width of the rectangle, what is the base and height of the triangles and what is the area of one of the triangles.
