Asked by Earl

if two trapezoids have the same area, do they have the same area?

Answers

Answered by Reiny
I would certainly say, YES
Answered by Earl
Sorry I meant "If two trapezoids have the same area, do they have the same perimeter?"
Answered by Earl
Reiny Thank you. lol
Answered by Reiny
NO, suppose you have two trapezoids, that have the same height, so that the
height is also one of the sides.

case 1: has two parallel sides of 8 and 6, and a distance of 5 units between them
area = (1/2)(8+6)(5) = 35
the perimeter is 8+5+6+√(5^2 + 2^2) = 19 + √29 = appr 24.385...

case 2: has two parallel sides of 10 and 4 and a distance of 5 units between them
area = (1/2)(10+4)(5) = 35 <----- same area
perimeter = 10 + 5 + 4 + √(5^2 + 6^2) = appr 26.81... , not the same

All I needed was ONE exception to the rule to say NO
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