Quadrilateral Shape

Quadrilaterals exhibit diverse shapes, ranging from the symmetrical squares and rectangles to the more complex and irregular parallelograms and trapezoids.

Trapezium

A trapezium is a quadrilateral that has one pair of opposite sides parallel. In a regular trapezium, non-parallel sides are equal, and its base angles are equal.

The area of trapezium is 1/2 × Sum of parallel sides × Distance between them.

Properties of Trapezium

Here are two important properties of a trapezium:

• The sides of the trapezium that are parallel to each other are known as the bases of trapezium. In the above image, AB and CD are the base of the trapezium.
• The sides of the trapezium that are non-parallel are called the legs. In the above image, AD and BC are the legs.

Area of Trapezium

The area of a trapezium can be calculated using the formula:

Area =1/2 ​× (a+b) × (h)

Where the parallel sides (a and b) are the two sides of the trapezium that are parallel to each other, and the height (h) is the perpendicular distance between these parallel sides.

Perimeter of Trapezium

The perimeter of a trapezium is the sum of the lengths of all its four sides.

If the trapezium has side lengths a, b, c, and d, then the perimeter is:

Perimeter = a+b+c+d

Kite

Kite has two pairs of equal adjacent sides and one pair of opposite angles equal. Diagonals of kites intersect perpendicularly.

The longest diagonal of the kite bisects the smaller one.

Properties of Kite

Let’s discuss some of the properties of a kite.

• A kite has two pairs of equal adjacent sides. For example, AC = BC and AD = BD.
• The interior opposite angles that are obtuse are equal; here, ∠A = ∠B.
• The diagonals of a kite are perpendicular to each other; here, AB is perpendicular to CD.
• The longer diagonal of the kite bisects the shorter diagonal. Here, CD bisects AB.

Area of a Kite

The area of a kite is calculated using the formula:

Area = ½ (d1 x d2)

where, d1 and d2 represent the lengths of the diagonals of the kite.

It’s important to note that this formula works regardless of whether d1 is longer or shorter than d2.

Perimeter of a Kite

The perimeter of a kite, which is the total length of all its sides added together, is calculated using the formula:

Perimeter = 2(a + b)

where, a and b represent the lengths of the two pairs of equal sides of the kite.

Parallelogram

Parallelogram is a quadrilateral whose opposite sides are equal and parallel. Opposite angles of a Parallelogram are equal, and its diagonals bisect each other.

Properties of Parallelogram

The properties of a Parallelogram are:

• The opposite sides of a parallelogram are parallel and equal. In the above example, AB and CD are parallel and equal, and AC and BD are parallel and equal.
• The opposite angles in a parallelogram are equal. ∠A = ∠D and ∠B = ∠C.
• The diagonals of a parallelogram bisect each other.

Area of a Parallelogram

The area of a parallelogram is calculated as the product of its base and height. The formula is given as:

Area of Parallelogram ​= base × height

Where the base is any one of the parallel sides, and the height is the perpendicular distance between the base and its opposite side.

Perimeter of a Parallelogram

The perimeter of a parallelogram is the sum of the lengths of all its sides. Since opposite sides of a parallelogram are equal in length, the perimeter is calculated as:

Perimeter of Parallelogram​ = 2 × (a+b)

Where, a and b are the adjacent sides of a parallelogram.

Rectangle

Rectangle is a quadrilateral whose opposite sides are equal and parallel and all the interior angles equal to 90°.

Diagonals of a rectangle bisect each other.

Note that all the rectangles are parallelograms, but the reverse of this is not true.

Rectangle Properties

These are some of the important properties of rectangle:

• The opposite sides of a rectangle are parallel and equal. In the above example, AB and CD are parallel and equal, and AC and BD are parallel and equal.
• All 4 angles of a rectangle are equal and are equal to 90°. ∠A = ∠B = ∠C = ∠D = 90°.
• The diagonals of a rectangle bisect each other and the diagonals of a rectangle are equal, here, AD = BC.

Area of a Rectangle

The area of a rectangle is calculated as the product of its length and width. The formula is given as:

Area of Rectangle​ = length × width

Where the length is the longer side and the width is the shorter side of the rectangle.

Perimeter of a Rectangle

The perimeter of a rectangle is the sum of the lengths of all its sides. Since opposite sides of a rectangle are equal in length, the perimeter is calculated as:

Perimeter of Rectangle​ = 2 × (length + width)

This formula doubles the sum of the length and width because each side is counted twice.

Rhombus

Rhombus is a quadrilateral that has all sides equal and opposite sides parallel. Opposite angles of a rhombus are equal, and diagonals of the Rhombus bisect each other perpendicularly. .

Note all rhombus are parallelograms, but the reverse of this is not true.

Properties of Rhombus

Here are some of the key properties of a Rhombus:

• All 4 sides of a rhombus are equal. AB = BC = CD = AD.
• The opposite sides of a rhombus are parallel and equal. In the image above, AB is parallel to CD and AD is parallel to BC.
• The diagonals of a rhombus Bisect each other at 90°.

Area of a Rhombus

The area of a rhombus can be calculated by multiplying the lengths of its two diagonals and dividing by 2. The formula is:

Area of Rhombus ​= 1/2 ​× (diagonal1 × diagonal2​)

Where, diagonal1 and diagonal2​ are the lengths of the two diagonals.

Perimeter of a Rhombus

The perimeter of a rhombus is the sum of the lengths of all its four sides. Since all sides of a rhombus are equal in length, the perimeter can be calculated as:

Perimeter of Rhombus​ = 4 × side

Where sideside is the length of any one of the sides.

Square

A quadrilateral that has all sides equal and opposite sides parallel and all interior angles equal to 90° is called a Diagonals of squares bisect each other perpendicularly. Note that all squares are rhombus but not vice-versa. 

Properties of Square

The properties of a square are:

• All four sides of a square are equal to each other.
• The interior angles of a square are 90°.
• The diagonal of a square bisects each other at 90°.
• The opposite sides are parallel, and the adjacent sides are perpendicular in a square.

Area of a Square

The area of a square is calculated by squaring the length of one of its sides. The formula is:

Area of Square​ = side²

Where sideside is the length of one side of the square.

Perimeter of a Square

The perimeter of a square is the sum of the lengths of all its sides. Since all sides of a square are equal in length, the perimeter can be calculated as:

Perimeter of Square​ = 4 × side

Where sideside is the length of any one of the sides.

Quadrilateral: A quadrilateral is a two-dimensional figure characterized by having four sides, four vertices, and four angles. It can be broadly classified into two categories: concave and convex. Within the convex category, there are several specific types of quadrilaterals, including trapezoids, parallelograms, rectangles, rhombi, and squares.

The sum of the interior angles of a Quadrilateral is 360°. Let’s learn what is a quadrilateral, its shapes, types, properties, formulas, and examples in detail.