[Maths Class Notes] on Quadrilateral Pdf for Exam

A quadrilateral is a plane closed geometric figure with four sides and four angles. A quadrilateral can be constructed using a compass and a ruler. There are several real-life examples of a quadrilateral: kites, squares, rectangles, rhombus, etc. The word quadrilateral is derived from the word “quad” which means four. Hence, there are four adjoining sides of a quadrilateral at all times.

Properties

• A quadrilateral always has four sides and four angles.

• The length of sides may be the same or different.

• The sum of all the internal angles will be 360°.

• The sum of all the external angles will also be 360°.

Construction

A quadrilateral can be constructed using a ruler and a compass if any of the following conditions are provided:

• Length of four sides and one diagonal are given

• Measurement of three sides and two angles are given

• Measurements of two sides and three angles are given.

Types

There are a lot of examples of a quadrilateral but the most common geometric figures are square, rectangle, rhombus, parallelogram and trapezium. Except for a trapezium, all the other figures have at least two parallel sides and every quadrilateral has four vertices, four sides and four angles.

Square has all four equal sides and angles. The diagonals of a square bisect each other at 90°. Both the opposite sides of the square are parallel to each other.

Rectangle has equal opposite sides and all four equal angles. The opposite sides of a rectangle are parallel to each other as well.

Rhombus has equal sides, and opposite sides are parallel to each other. Opposite angles are equal and the sum of two adjacent angles is 180°. The diagonals from opposite sides of a rhombus bisect each other and are perpendicular to each other.

A parallelogram has two opposite and equal sides which are also parallel to each other. The opposite angles are equal and the diagonals bisect with each other.

Trapezium has only one opposite parallel and the diagonal bisectors are of the same ratio.

Quadrilaterals can be further classified as convex quadrilateral, concave quadrilateral and intersecting or crossed quadrilaterals based on the diagonals former inside a quadrilateral. In convex quadrilaterals, the diagonals are completely within the boundary of the quadrilateral while in concave quadrilaterals, the diagonals are partially outside the boundary of the quadrilateral.

Formulas

There are two basic formulas of quadrilaterals, namely: area and perimeter.

Area

• Area of square: side×side

• Area of rectangle: length×breadth

• Area of parallelogram: base×height

• Area of rhombus: ½× (first diagonal length)×(second diagonal length)

• Area of trapezium: ½× (length of first diagonal)×(length of second diagonal)

Perimeter

• The perimeter of square: 4×length of side

• The perimeter of rectangle: 2×(length of breadth + length of a side)

• Perimeter of parallelogram: 2×(base+side)

• The perimeter of rhombus: 4×length of side

• The perimeter of trapezium: 2×(a+b), a and b are lengths of adjacent sides.

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