Grade 7 - Area and Perimeter Challenge
Makunja Challenge
Find the ratio of the area to the perimeter of a square with a diagonal of 32cm.
(mathcounts)
(mathcounts)
The length of rectangle A is
1
the length of rectangle B, and the width of rectangle A is twice the width of B. What is the
3
ratio of area of A to the area of B?
(Math Workout for the new SAT)
The diagram shows a rectangle that has been dissected into nine non-overlapping squares. Given that the width and the
height of the rectangle are positive integers with greatest common divisor 1, find the perimeter of the rectangle. (from
the 2000 American Invitational Mathematics Examination)
SOLUTION https://www.youtube.com/watch?v=1uWZNW5PF-s#t=237
If you fold a square paper vertically, the new rectangle has a perimeter of 39 inches. What is the
area of the original square?
What is the perimeter of the original square?
What is the area of the resulting rectangle?
Make a ratio of areas and perimeters. What do you notice?
http://www.fi.edu/school/math2/sept.html#measure
This will really challenge you...
Better Buy
Mr. and Mrs. Simpleton are shopping for carpet for their living room and dining room. Their living
room is 21 feet by 15 feet and their dining room is 12 feet by 9 feet. They have looked at two
different priced carpets. One for $14.95 a square yard installed and another for $19.99 a square
yard installed. How much would they save by choosing the cheaper carpet? What are some other things besides money
that they should consider before making their choice? After you find out how much carpet they need, figure out the
savings in one calculation. Explain.
http://www.fi.edu/school/math2/sept.html#measure