No, they are not equal.
Say a rectangle is 3 x 2 = 6 sq in area
Say another is 6 x 1 = 6 sq in area
perimeter of first one is 2L + 2B = 10
perimeter of second one is 2L + 2B = 14
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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'
Yes, it can because a 3 by 6 rectangle has the perimeter of 18 and has the area of 18! :)
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.
Yes. Say there are two rectangles, both with perimeter of 20. One of the rectangles is a 2 by 8 rectangle. The area of this rectangle is 2 x 8 which is 16. The other rectangle is a 4 by 6 rectangle. It has an area of 4 x 6 which is 24.