July 25 - August 11, 2000 - Swarthmore, Pennsylvania

2000 Summer Institute || Agenda || List of Participants

Tim's Solution

From: Tim, age 15, class: 9 geometry

Answer:

The answer to this problem is 81.

Explanation:

First you find the the sides of the two given squares which are 7
times 5 and 2 times four. From there you can find the area of the
other 2 boxes by multiplying 4 and 7,and 2 and 5.Then you add all
the products together 35, 28, 10, 8 which equals 81.

Brian's Solution

 
From: Brian, age 15, class: Geometry 

Answer:

The area of the square is 86.

Explanation:

I added 35 and 35 and got 70 and then I added 8 and 8 and I got 16
and then  I added and got 86.

Mary's Solution

From: Mary, age 15, class: 10

Answer:

The area of the square is 81.

Explanation:

I used quess and check.

Konrad's Solution

From: Konrad, age 13, class: Geometry

Answer:

The area of the square is 77 sq units.

Explanation:

I got the factors of 35 = 1,5,7,35
and the factors of8  = 1,2,4,8

And worked it out getting 5,7  2,4

5*4 = 20
7*2 = 14

35+8+20+14=77

Michael's Solution

From: Michael, age 16, class: Advanced Geometry

Answer:

I concluded that the final area of the square is 81.

Explanation:

I first decided that to be a square both sides of the square had to be
equal. So I first set the part of the square that equaled 35 in area
to the top and bottom equaling 7, and the two sides equaling 5. I then
tried to think of two numbers that eight was divisible by to see if
they were able to add with the two numbers of the section of the
square that equals 35. I  came up with 4, for the two sides, and 2 for
the bottom and top. This meant that the distance from one side of the
square was 9 by 9. I then multiplied 9 and 9 together to get the whole
area of the square and this equaled 81, the solution. I found another
solution also. I set the smaller square in the bottom right corner to
1/2 on the sides, and 16 on the bottom and top. I then did the same
process and came up with 17 and 1/2 for the two sides of the upper
right section, and 2 for the bottom and top of the shape. This meant
that the distance across the whole side was 18. 18^2 equals 324, the
area of the other square, and the other solution.

Sarah's Solution

From: Sarah, age 15, class: 10/Geometry

Answer:

The area of the whole square is 86^2.

Explanation:

First, I saw that the square was divided in 2 pairs of congruent
sections.  The section with 35^2 area was congruent to the section
below it.  And the section with 8^2 area was congruent to the section
above it.  I simply concluded that if you added the given areas with
the conjectured areas, they would add up to the total area of the
whole square, which was 86^2.