yes. for example imagine a cube with a length of five on all sides. its perimeter would be 20 and its area 25. now make it a rectangle with 6 as two lengths and 4 as two lengths. its perimeter is 20 but its area is 24
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That depends on the exact shape. For the same area, you can have different perimeters, depending on the shape.
The area doesn't tell you the perimeter. There are an infinite number of different shapes and different dimensions that all have the same area but different perimeters. Here are a few 1/4-acre rectangles, and their perimeters: 90-ft x 121-ft . . 422-ft 30' x 363' . . . . . 786' 15' x 726' . . . . 1,482' 10' x 1,089' . . . 2,198' 6' x 1,815' . . . . 3,642' 2' x 5,445'. . . . 10,894'
24
I don't know about the relation in the perimeters of a triangle and a parallelogram but if a triangle is on the same base on which the parallelogram is and the triangle is between the same parallel lines of the parallelogram, then the area of the triangle will be half the area of the parallelogram. That is, area of a triangle = 1/2 area of a parallelogram if the triangle is on the same base and between the same parallel lines.
If it's a circle or a square, no problem, but a rectangle can have different length & width but the same area eg 4 x 6, 3 x 8 or 2 x 12 which have respective perimeters of 20, 22 and 28.