What is a quadrilateral?
A quadrilateral is a polygon that has four sides. We have seen many examples of quadrilaterals in our daily life such as the surfaces of a table, a book, a laptop and many other objects.
Area of Quadrilateral
The area of a quadrilateral is the region covered by the boundaries of the quadrilateral.
Formula for the Area of a Quadrilateral
We use different formulas to calculate the area of different types of quadrilaterals.
- Area of a Parallelogram
A parallelogram is a quadrilateral whose opposite sides are equal and parallel to each other. The area of a parallelogram is the product of its base and height.
Area of a parallelogram: A = bh, where h is the height and b is the base of the parallelogram.
- Area of a Rectangle
A rectangle is a quadrilateral in which the opposite sides are equal and parallel to each other. The sides also make a right angle at the point where they intersect. The area of a rectangle is the product of its length and width.
Area of a rectangle: A = lw, where l is length and w is width.
- Area of a Square
A square is a type of quadrilateral in which all sides and all angles are equal. The area of a square is obtained by multiplying the length of a side by itself.
Area of a square: A = \(s^2\), where s is the side length of a square.
- Area of a Trapezoid
A trapezoid is a quadrilateral with one pair of opposite sides that are parallel to each other. The area of a trapezoid is half the product of the height and the sum of the lengths of the parallel sides.
Area of Trapezoid: A = \(\frac{1}{2}\)h(a + b), where h is height, a and b are the length of parallel sides.
- Area of a Kite
A kite is a quadrilateral that has two pairs of adjacent sides that are equal in length and the opposite sides are of different lengths. The area of the kite is the sum of the area of two triangles formed by a diagonal.
Area of kite: A = \(\frac{1}{2}\) h(b + a) + \(\frac{1}{2}\) H(b + a), where h and H are the height of bigger and smaller triangles and (a + b) is the length of the diagonal by which these triangles have been created.
- Area of a Rhombus
A rhombus is a quadrilateral where all sides are equal, but its diagonals are different in measurement. The area of a rhombus is half of the product of its diagonals.
- Area of Rhombus: A = \(\frac{1}{2}d_1 d_2\) where \(d_1\) and \(d_2\) are the diagonals of the rhombus.
Solved Examples
Example 1: Find the area of the parallelogram in the image.
Solution:
A = bh [Formula for the area of a parallelogram]
= 8 (18) [Substitute the values]
= 144 [Multiply]
So, the area of the parallelogram is 144 square yards.
Example 2: The area of the given rectangle is 240 \(cm^2\). Find the width of the rectangle.
Solution:
The length is 18 cm and area is 240 \(cm^2\).
A = l \(\times\) w [Formula for the area of a rectangle]
240 = 18 \(\times\) w [Substitute the values]
w = \(\frac{240}{18}\) [Divide]
w = 13.33 [Simplify]
So, the width of the rectangle is 13.33 cm.
Example 3: Tom was studying geometrical shapes and found a trapezoid with an area of 140 \(cm^2\) and the length of the parallel sides is 12 cm and 16 cm. Find out the height of the trapezoid.
Solution:
As stated, the area of the trapezoid is 140 \(cm^2\) and the length of parallel sides is 12 cm and 16 cm.
A = \(\frac{1}{2}\) h(a + b) [Formula of area of trapezoid]
140 = \(\frac{1}{2}\) h(16+12) [Substitute the values]
h = \(\frac{140\times 2}{28}\) [Simplify]
h = 10 cm
So, the height of the trapezoid is 10 cm.
Example 4: Annie was playing on a carrom board, a square-shaped board of area 2500 cm2. Find the length of one side of the carrom board.
Solution:
The area of carrom board is 2500 \(cm^2\)
A = \(s^2\) [Formula for area of square]
2500 = \(s^2\) [Substitute the value]
s = \(\pm 50\) [Taking square root]
So, the length of the side of the carrom is 50cm because length cannot be negative.
Quadrilaterals are important geometrical closed shapes with four sides, four vertices and four angles.
The different types of quadrilaterals are rectangles, squares, parallelograms, rhombuses, kites and trapezoids.
The sum of interior angles of a quadrilateral is 360 degrees.
Some real life examples of quadrilaterals are the top of books, the screen of a laptop, a carrom board or even a TV screen.
Square inches, square feet, square miles, square centimeters, square meters and square kilometers are a few examples of the units used to represent the area of a shape.