Question

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

Answer 1

I would certainly say, YES

Answer 2

Sorry I meant "If two trapezoids have the same area, do they have the same perimeter?"

Answer 3

Reiny Thank you. lol

Answer 4

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