Question
if two trapezoids have the same area, do they have the same area?
Answers
Reiny
I would certainly say, YES
Earl
Sorry I meant "If two trapezoids have the same area, do they have the same perimeter?"
Earl
Reiny Thank you. lol
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
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