What Quadrilaterals have a perpendicular diagonals?
The quadrilaterals that have perpendicular diagonals, meaning they intersect at 90° angles, are a square, a rhombus, and a kite.
What is the formula of quadrilateral area?
Area of General Quadrilateral Formula = 1/2 x diagonals length x ( sum of the height of two triangles ).
How do you find the diagonal of a quadrilateral?
If we suppose the length of a square is L, then the length of the diagonal = L √2. Area of a square = L2. A quadrilateral whose four sides are all congruent in length is a rhombus.
How do you find the area of a quadrilateral with 4 sides?
Example: A four-sided shape has two adjacent sides with lengths of 4 meters. You can find the area of this square by multiplying its base times its height: 4 × 4 = 16 square meters….Parallelograms include:
- Squares: Four sides, all the same length.
- Rectangles: Four sides; opposite sides have same lengths.
Can Quadrilaterals have a perpendicular diagonals?
The diagonals of a convex quadrilateral are perpendicular if and only if the two bimedians have equal length. A convex quadrilateral is orthodiagonal if and only if its Varignon parallelogram (whose vertices are the midpoints of its sides) is a rectangle.
What Quadrilaterals have no perpendicular diagonals?
As diagonals are not perpendicular, it cannot be a square or rhombus (latter does not have congruent diagonals). Hence, quadrilateral is a rectangle.
Can we conclude that if the diagonals of any quadrilateral are perpendicular then its area is half the product of its diagonals?
Proof : Since the diagonals AC and BD of quadrilateral ABCD bisect each other at right angles. Thus , ABCD is a quadrilateral whose diagonals bisect each other at right angles and all four sides are equal. Hence , ABCD is a rhombus. now it is proved tha ABCD is a rombus and area of Rombus =1/2 product of diagonals.
Which quadrilateral has equal diagonals?
A parallelogram with one right angle is a rectangle. A quadrilateral whose diagonals are equal and bisect each other is a rectangle.
How many diagonals are there in the quadrilateral?
2
Solved Examples
| Polygon Name | Number of Sides | Number of Diagonals |
|---|---|---|
| Quadrilateral | 4 | 2 |
| Pentagon | 5 | 5 |
| Hexagon | 6 | 9 |
| Heptagon | 7 | 14 |
What is the formula of a diagonal?
The formula to calculate the number of diagonal of an n-sided polygon = n(n-3)/2 where n is the number of sides of the polygon.