Quadrilateral Formulas

There are two basic formulas for quadrilaterals, that are:

• Area 
• Perimeter

Area of Quadrilateral

The area of the quadrilateral is the total space occupied by the figure. The area formula for the different quadrilaterals are given below:

Perimeter of Quadrilateral

Perimeter is the total distance covered by the boundary of a 2d shape. Since we know the quadrilateral has four sides, therefore, the perimeter of any quadrilateral will be equal to the sum of the length of all four sides. If ABCD is a quadrilateral then, the perimeter of ABCD is:

Perimeter = AB + BC + CD + AD

Important Facts of Quadrilateral

• A quadrilateral is a trapezoid or a trapezium if 2 of its sides are parallel to each other.
• A quadrilateral is a parallelogram if 2 pairs of sides parallel to each other.
• Squares and Rectangles are special types of parallelograms. Below are some special properties.– All internal angles are of “right angle” (90 degrees).– Each figure contains 4 right angles.– Sides of a square are of the same length (all sides are congruent) – Opposite sides of a rectangle are the same.– Opposite sides of a rectangle and square are parallel.
• A quadrilateral is a rhombus, if
  • All the sides are of equal length-specified 2 pairs of sides are parallel to each other.
• A kite is a special sort of quadrilateral, in which 2 pairs of adjacent sides are equal to each other.

Quadrilaterals Solved Examples

Example 1: What is the base of a rhombus, if its area is 40 square units and the height is 8 units?
Solution:
Given,
Area = 40 square units
Height = 8 units
Area of rhombus = Base × Height
40 = Base × 8
Base = 40/8 = 5 units

Example 2: If 15 metres and 6 metres are diagonal lengths of a  kite, then what is its area?

Solution: Given, diagonal 1 = 15 metre and diagonal 2 = 6 metre. So, the area is simply calculated as, (1/2)(15×6) = 45 m².

Example 3: Find the perimeter of the quadrilateral with sides 5 cm, 7 cm, 9 cm and 11 cm.

Solution: Given, sides of a quadrilateral are 5 cm, 7 cm, 9 cm and 11 cm.

Therefore, perimeter of quadrilateral is:

P =  5 cm + 7 cm + 9 cm + 11 cm = 32 cm

Example 4: The perimeter of the quadrilateral is 50 cm and the lengths of the three sides are 9 cm, 13 cm and 17 cm. Find the missing side of the quadrilateral.

Solution: Let the unknown side of the quadrilateral = x

Given, Perimeter of the quadrilateral = 50 cm

The lengths of other three sides are 9 cm, 13 cm and 17 cm

As we know,

Perimeter = sum of all the four sides.

50 = 9 cm + 13 cm + 17 cm + x

50 = 39 + x

x = 50 – 39

x = 11

Therefore, the fourth side of quadrilateral = 11 cm

Practice Questions on Quadrilaterals

1. What is the area of a square with a side length equal to 13 cm?
2. What is the perimeter of rectangle if length = 14cm and breadth = 10 cm?
3. The angles of a quadrilateral are in the ratio 3 : 5 : 9 : 13. Find all the angles of the quadrilateral.