Quant Study Notes: Area & Polygons |

Polygon and quadrilateral’s properties

1. Polygon: – It is a closed plane figure bounded by three or more than three straight lines.

There are of two types of polygons.

Convex: A polygon in which none of its interior angle is more than 180°

Concave: A polygon in which at least one interior angle is more than 180°.

Regular Polygon: All the sides are equal and also all the interior angles are equal

Sum of Interior angles of a polygon = (n – 2) × 180

n → number of sides

Sum of exterior angle = 360

2. Rectangle: –

In a parallelogram with two adjacent angles A and B equal to each other, then the parallelogram is a rectangle or a square.
Diagonals are equal and bisect each other, but not necessarily at right angles.
For the given perimeter of rectangle, a square has maximum area.
The figure farmed by joining the mid-points of the adjacent sides of rectangle is a rhombus.
The quadrilateral formed by joining the mid points of intersections of the angle bisectors of a parallelogram is a rectangle.

3. Rhombus: –

A parallelogram in which all sides are equal is called a rhombus.
Diagonal of rhombus bisect each other at right angles, but they are not necessarily equal.
Diagonal bisect the vertex angles.
Sum of any two adjacent angles is 180°
Figure formed by joining the mid-points of the adjacent sides of a rhombus is a rectangle