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Q: Is a diagonal of a square perpendicular to its side always?

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No.

Not always, the diagonal can be figured out using the Pythagorean Theorem (a²+b²=c²). Where the diagonal is the hypotenuse (c). By rearranging the Pythagorean Theorem, you can see that the diagonal of a square is always 1.4 times the side of the square.

Yes, each of the four sides will be perpendicular with the opposite side.

14 The ratio of the side of a square to the diagonal is 1.4.

As a square has right angles, the diagonal forms a right triangle with two of the sides of the square. Therefore use Pythagoras: diagonal² = side² + side² → diagonal² = 2side² → diagonal = side × √2 Therefore to find the length of the diagonal of a square, multiply the side length of a square by the square root of 2.

The side lengths of a square with a diagonal of 16 is: 11.31.

The diagonal of a square 2.0 meters on a side is: 2.828 meters.

side of a square is diagonal / 21/2

The diagonals of a square are congruent, bisect each other, perpendicular, and either diagonal's length is sqrt(2) times any side length.

Divide the length of the diagonal of a square by 1.4142 (which is the square root of 2) to find the length of a side. Similarly, to find the length of the diagonal of a square, multiply the length of a side by 1.4142.

The diagonal is 33.941 units.

Using Pythagoras: diagonal² = side² + side² = 2 × side² → side² = diagonal² ÷ 2 area = side² = diagonal² ÷ 2 = 14² ÷ 2 = 98 units²

The answer in 6.... draw an angular bisector from one of the angles to the centre of circle then draw a perpendicular from the centre of circle. Those to lines will form a triangle... use trigonometry and find the length of the perpendicular, which is also a radius... double the radius and u will get the diagonal for the square... using formula :- (Side)^2 + (Side)^2 = (Diagonal)^2, find the side of square and square the answer, which will give you your final answer

56.568542494923801952067548968388

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

Using Pythagoras: diagonal² = side² + side² = 2 × side² → side² = diagonal² ÷ 2 area = side² = diagonal² ÷ 2 → diagonal² = 2 × area → diagonal = √(2 × area) = √(2 × 36) = 6√2 ≈ 8.49

The diagonal is 21.21 decimeters.

The diagonal of a square = the length of one side x the square root of 2 (approx 1.414)

The length of one side of a square with a 16-centimeter diagonal is: 11.31 cm

Using Pythagoras' theorem the diagonal is 16 times the square root of 2

Half its diagonal is 0.919 meters.

The diagonal is 60*sqrt(2) = 84.853 units.

The diagonal length = 7.07 inches.

If the circle is inscribed in the square, the side length of the square is the same as the diameter of the circle which is twice its radius: → area_square = (2 × 5 in)² = 10² sq in = 100 sq in If the circle circumscribes the square, the diagonal of the square is the same as the diameter of the circle; Using Pythagoras the length of the side of the square can be calculated: → diagonal = 2 × 5 in = 10 in → side² + side² = diagonal² → 2 × side² = diagonal² → side² = diagonal² / 2 → side = diagonal / √2 → side = 10 in / √2 → area _square = (10 in / √2)² = 100 sq in / 2 = 50 sq in.

About 84.85 units.