![]() ![]() Here, 'n' represents the number of sides of the polygon. The formula that is used to find the number of diagonals in a polygon is, The number of diagonals in a polygon differs according to the type of polygon, based on the number of sides. The body diagonal of a cuboid is the one that cuts through the center of the cuboid while the face diagonal is the one joining the opposite vertices on every face. While the face diagonal is the one joining the opposite vertices on every face.Ī cuboid is a three-dimensional form of a rectangle. The body diagonal of a cube is the line segment that cuts through its center, joining the opposite vertices. This means that the length, width, and height of a cube are equal, and all its faces are squares. Diagonals of a CubeĪ cube is a three-dimensional solid figure, also known as a square solid that has edges of the same length. Let us learn more about the diagonal of a cube and the diagonal of a cuboid. The number of diagonals and their properties vary for different solids, based on the number of edges. Since they are three-dimensional figures, they have body diagonals (space diagonals) and face diagonals. Just like polygons, 3D shapes also have diagonals. A hexagon has 9 diagonals as shown in the following figure. The length of all six sides is equal in a regular hexagon. A pentagon has 5 diagonals as shown in the figure given below.Ī hexagon is a closed two-dimensional figure with six sides and six corners. The length of all five sides is equal in a regular pentagon. A rhombus can be defined as a diamond-shaped quadrilateral having four equal sides.Ī pentagon is a closed two-dimensional figure with five sides and five corners. The diagonals of a rhombus are the line segments joining the opposite vertices, bisecting each other at a 90° angle, which means that the two halves of any diagonal will be of the same length. A diagonal divides a rectangle into 2 right triangles, and the diagonals become the hypotenuse of these right-angled triangles. We can see that AC and BD are of the same length. ![]() Observe the following rectangle, in which AC and BD are the diagonals. The diagonal of a rectangle is a line segment that joins any two of its non-adjacent vertices. One diagonal of a square divides it into two equal right triangles, such that the diagonal becomes the hypotenuse of the right-angled triangles so formed.The length of the diagonals AC and BD in the given square is the same.By joining the opposite vertices, we get two diagonals, AC and BD.The number of diagonals of a square = 2.Observe the following square and its diagonals to relate the facts given below: The diagonal of a square is a line segment that joins any two of its opposite vertices. The opposite sides are parallel to each other and all the sides are of equal length. Diagonals of a SquareĪ square is defined as a closed two-dimensional figure having four sides and four corners. In other words, there are 2 diagonals in a quadrilateral, whether it is a square, a rectangle, or a rhombus. We know that a quadrilateral is a four-sided polygon which means that if we join the two opposite vertices in it we get to form 2 diagonals and not more than that. In other words, there are no diagonals in a triangle. Therefore, the number of diagonals of a triangle = 0. It means that there are no line segments that can form diagonals. No vertices in a triangle are non-adjacent. Diagonals of a TriangleĪ triangle is defined as a closed shape that has 3 sides, 3 angles, and 3 vertices. Let us now learn more about the diagonals of different polygons. Depending upon the type of polygon and the number of sides, the number of diagonals and their properties vary. The diagonal of a polygon is a line segment that connects any two non-adjacent vertices. ![]()
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