Homework: Area and Perimeter.

Complete the following, then view the solutions to check your answers. 

A.  Use the Java applet below to answer each of the following questions.  

http://www.mste.uiuc.edu/activity/boxperim/  

1.  Place four squares on the board so that none of them are touching.  What is the total area?  What is the total perimeter?

2.  Move the four squares so that they form a 1 x 4 rectangle.  Did the area change?  What is the perimeter now?

3.  Move the four squares so that they form a larger square.  Did the area change?  What is the perimeter now?

4.  Place twelve squares on the board to form a 1 x 12 rectangle.  What is the area? What is the perimeter?

5.  Move the squares so that they form a 2 x 6 rectangle.  Did the area change?  What is the perimeter now?

6.  Move the squares so that they form a 3 x 4 rectangle.  Did the area change?  What is the perimeter now?

7.  Recognizing that inductive reasoning might lead us astray at times, what conclusions about the area and perimeter of rectangles could you reach from the limited number of trials given above?

B.  Use the Java applet below to answer each of the following questions.

http://nlvm.usu.edu/en/nav/frames_asid_282_g_3_t_3.html?open=activities

1.  Use one rubber band to build a right isosceles triangle with legs that are four units long.  Use the grid to count the area of this triangle; count the 1/2 squares by adding pairs of them together.   

2.  Use a second rubber band to build another right isosceles triangle that would complete the first one by turning it into a square.  The second triangle should be "upside down" and share its hypotenuse with the first one.  Can you use this picture to help explain the formula for the area of a triangle?

3.  Clear the applet and build a parallelogram so that you can easily count the area.  Some parallelograms are easier than others to count.  Work until you find a "nice" one.  What is its area?

4.  Use additional rubber bands to form two right triangles to explain the formula for the area of a parallelogram in terms of the area formula for a rectangle.

5.  Use one rubber band to build an obtuse triangle so that you can easily count the area.  Some obtuse triangles are easier than others to count.  Work until you find a "nice" one.  What is its area?

6.  Use another rubber band to complete the obtuse triangle by turning it into a parallelogram. Can you use this picture to help explain the formula for the area of a triangle in terms of the area formula for a parallelogram?