if two trapezoids have the same area, do they have the same area?
I would certainly say, YES
Sorry I meant "If two trapezoids have the same area, do they have the same perimeter?"
Reiny Thank you. lol
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
Yes, two trapezoids with the same area will have the same area. However, I believe there might be a typo in your question. Let me explain the concept of trapezoids and their areas.
A trapezoid is a quadrilateral (a four-sided polygon) with one pair of parallel sides. The line segments that connect the parallel sides are called the legs, and the other two sides are called the bases. The height of a trapezoid is the perpendicular distance between the bases.
To calculate the area of a trapezoid, you can use the formula:
Area = (base1 + base2) * height / 2
Now, coming back to your question, if two trapezoids have the same area, it means that the product of the sums of their bases (base1 + base2) multiplied by their height divided by 2 will be equal for both trapezoids. Therefore, the two trapezoids will indeed have the same area.