Using an 8x10 sheet of paper, divide into three to six
sections of equal area.
no more than two sections may have the same perimeter.
you must show your calculations and they must be
accurate.

See picture below

Step-by-step explanation:

The total area of the sheet of paper is 80, so we can divide the sheet of paper into 4 different sections, each one of them with area 20 (you can verify this by counting the squares in each section, there are 20 squares per section).

In the picture below we can see that the perimeter of each of the sections are from left to right:

The first one is a rectangle, with sides 5 and 4. Therefore the perimeter is 2(5) + 2(4) = 18.

The next section is irregular so we sum up the sides: 2 + 6 + 5 + 1 + 2 + 1 + 5 + 4 = 26.

For the next section we also sum up the sides: 3 + 7 + 2 + 1 + 1 + 6 = 20.

For the bottom section, we will sum up the sides too: 2 + 1 + 6 + 1 + 2 + 1 + 10 + 3 = 26.

So the perimeters are 8, 26, 20 and 26. This satisfies the condition of no more than two sections having the same perimeter.

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