If two trapezoids have the same area, do they always have the same perimeter? Explain your thinking with words and diagrams.
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*
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
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 asf.
I cringe.
Yes, for you can have different lengths for each base and different heights, but get the same same area with a different perimeter.
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!!!
The answer is no it doesn't
Umm I'm tryna figure that out but this web isn't really helpin moi
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 it’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