# Math

If two trapezoids have the same area, do they always have the same perimeter? Explain your thinking with words and diagrams.

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1. Go to en wikipedia
and type: Trapezoid

You can construct many trapezoides with some area but different perimeter.

Area of trapezoid=((a+b)/2)*h

Example:

a+b=10 h=6 A=30

a+b=2 h=30 A=30

a+b=12 h=5 A=30

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2. No. You can construct many trapazoids with the same area with multiple side lengths, thus as perimeter is the addition of the outer side lengths of a figure, if two trapazoids have different side lengths but the same area, most of the time, the different side lengths will equal to different perimeters. Eg.

Trapazoid 1:
a=4 b=8 h=6
A=(a+b)xh/2)
=(4+8)x6/2)
=12x6/2
=72/2
=36units squared

side lengths=4 each
P=(a+b+side length)x2
=(4+8+4)x2
=16x2
=32units squared*

Trapazoid 2:
a=4 b=5 h=8
A=(a+b)xh/2
=(4+5)x8/2
=9x8/2
=72/2
=36units squared

side lengths=6&7
P=a+b+6+7
=4+5+6+7
=22units squred*

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3. yes this is correct the answer is

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4. If two trapezoids have the same area do they always have the same perimeter

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5. Umm I'm tryna figure that out but this web isn't really helpin moi

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6. the correct anwser is fuddi

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7. This isn't a solution to the question, just wanted to point out that the question was copied and pasted from the Grade 7 Nelson Math Textbook. Also, please STOP putting memes into the response. It's not that funny, and makes you look rude .
I cringe.

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8. Not necessarily

If a trapezoid has two bases, 3 and 3 and a height of 2 3+3 is 6 and times two divided by two cancel each other out so itâ€™s 6

If another trapezoid had two bases, 1 and 2 and a height of 4 1+2 is 3 times 4 is 12 divided by 2 which is also 6

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9. I agree with this! A trapezoid can have the same area with another one, but have different lengths and widths. It can have a different perimeter!!!

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10. Yes, for you can have different lengths for each base and different heights, but get the same same area with a different perimeter.

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