Where ‘p’ is the unknown diagonal length, q is the given diagonal length, ‘a’ and ‘b’ are the length and breadth of the parallelogram, respectively.Ī diagonal can also be situated outside the polygon. Length of diagonal = p = sqrt (2a 2 + 2b 2 – (q) 2 ) The length of one diagonal of a parallelogram can be determined if the dimensions of its sides and the length of the other diagonal is provided. The two diagonals of a parallelogram bisect each other, and the opposite sides and angles of any parallelogram are congruent. The formula for the length of one diagonal of a rhombus is : p= 2(a)/qĪ parallelogram is a rectangle with its angles not equal to 90 degrees. When all the angles of a rhombus become 90 degrees, then the rhombus turns into a square.Īrea of rhombus= A= (PQ)/2 where ‘p’ and ‘q’ are the lengths of diagonals of the rhombus To find the diagonal of the rectangle provided that we have the dimensions of its sides, we can use the diagonal formula of the rectangle.ĭiagonal of rectangle = sqrt (a 2 + b 2 ), where ‘a’ is the length of the rectangle and ‘b’ is the breadth (width) of the rectangle.Ī rhombus has four sides with two diagonals. Two congruent right triangles are obtained if the diagonal bisects a rectangle. Their diagonals are also congruent to each other and bisect each other. Rectangles are similar to squares therefore, they also have two diagonals. The diagonal formula of square =a/sqrt (2) where a is the length of any one of the sides of the square. To find the diagonal of a square, we use the given formula.
The length of the diagonal of a square can be found easily if we have the length of its side. The length of the diagonal of the square is also the length of the hypotenuse of the right triangle. Therefore, the two right triangles thus obtained have the same area and each triangle has half the area of the square. The diagonal is divided into two equal parts when the diagonals intersect each other.Įach of the diagonals divides the square into two congruent isosceles right triangles because when the diagonals intersect each other, they do so perpendicularly. Thus, they are also called congruent diagonals.Įach diagonal bisects the other. The diagonals of a square are of the same length. The diagonal of a square is the line segment that is drawn between its opposite corners. You will use diagonals not only in Math but also in your everyday life!Ī square has two diagonals. Huge steel rods are also placed diagonally in very tall or heavy buildings to prevent them from falling or crashing on itself. We put rods diagonally in an empty frame to stabilize it and keep it from breaking. Similarly, we can calculate for the other polygons.ĭiagonals make the framework or base for any structure. Therefore, there are 9 diagonals present in a hexagon. Number of diagonals= (n(n-3))/2 where n is the number of vertices of the polygonĮxample- To calculate the number of diagonals of a hexagon, we take n=6 (because it has 6 vertices) There is a simple formula to determine the number of diagonals in a polygon. The number of diagonals of a polygon depends on the number of sides it has. (plural- vertices) It is described as the corner of any shape. Examples- square, triangle, rectangle, decagon. The corners of a polygon are connected by line segments. It is a plane figure with three or more sides and angles. Here you can read about diagonals, the formula to calculate the number of diagonals, diagonal of square formula, diagonal of rectangle formula, diagonals of rhombus and parallelogram, and some fun properties of diagonals. A diagonal is defined as a line segment joining the two opposite vertices of a polygon.
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