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Yes, but only when the shape is a rectangle (or square). Other paralleograms will have one diagonal longer than the other. And yes, rectangles and squares ARE parallelograms.
The diagonal line of a rectangle for example is greater than its length.
One diagonal of a rhombus is larger than the other diagonal but both diagonals intercept each other at right angles.
rectangle/oblong
It could be a diagonal line of a polygon with more than 3 sides
Any shape other than a cube.Any shape other than a cube.Any shape other than a cube.Any shape other than a cube.
As no shape has been given for the area it is impossible to given the length of the diagonal - the diagonal can be ANY length greater than 0 (assuming you can define what diagonal means for the shape). If you are referring to a square with an area of 11 square inches then: Using Pythagoras: diagonal² = side² + side² = 2 × side² → side² = diagonal² ÷ 2 area = side² = diagonal² ÷ 2 → diagonal² = 2 × area → diagonal = √(2 × area) = √(2 × 11 sq in) = √22 in ≈ 4.69 in If you mean an 11 inch square, ie a square with 11 inches along each side: Use Pythagoras: Diagonal² = √(2 × sidelength²) → diagonal = side_length × √2 → diagonal = 11 in × √2 ≈ 15.6 in
On squares and rectangles, yes. But on parallelograms and rhombus the one diagonal can be shorter than one of the sides.
No
A line that joins any vertex of a polygon (or polyhedron) to any vertex other than itself or adjacent ones is a diagonal.
While only visualizing it and not bothering to draw it, it seems to us thatany diagonal of any regular polygon with more than 3 sides is longer thanany side.
You don't - you need additional information. Many different rectangles can have the same diagonal. If you know the diagonal and one side (which must be LESS than the diagonal), you can use Pythagoras' Theorem to calculate the other side.