Area of a quadrilateral - Definition with Examples
A quadrilateral is a polygon we obtain by joining four vertices, and it has four sides and four angles. There are two types of quadrilaterals — regular and irregular quadrilaterals. Some examples of the quadrilaterals are square, rectangle, rhombus, trapezium, and parallelogram.
Draw a diagonal AC connecting two opposite vertices of the quadrilateral ABCD.
Draw a perpendicular each from the other two vertices
(B and D) on the diagonal AC.
The area of the quadrilateral will be:
Area of quadrilateral ABCD = Area of △ABC + Area of △ADC
So, area of quadrilateral ABCD = (½ × AC × BE) + (½ × AC × DF)
To evaluate the area of a parallelogram, draw a perpendicular from one of the vertices to the base. This perpendicular is the height. Thus, the area will be the product of base and height.
Area of parallelogram = base x height
To find the area of a rhombus, we divide the quadrilateral into two equal isosceles triangles using the two diagonals. In the given rhombus ABCD, the point of intersection of these diagonals is E. Thus the area of the rhombus is:
Area of rhombus ABCD = Area of △ABC + Area of △ADC
⟹ Area of rhombus ABCD = (½ x AC x BE) + (½ x AC x ED)
⟹ Area of rhombus ABCD = ½ x AC (BE + ED)
⟹ Area of rhombus ABCD = ½ x AC x BD
Using this relationship we can also find the area of a square ABCD
Area of square ABCD = Area of △ABC + Area of △BCD
⟹ Area of △ABC = ½ * AC * AB
⟹ Area of △ABC = ½ * AC * AC (as AC = AB)
⟹ Area of △ABC = ½ * AC2
Similarly, Area of △BCD = ½ * CD2
Since, AC = CD, Area of △BCD will be ½ * AC2
Thus, area of square ABCD = 2 * (½ * AC2) = AC2
Hence, Area of square ABCD is the square of the side.
The area of a rectangle using the above formula will yield the product of its two adjacent sides, base and height. We represent it as:
The real-life application of quadrilaterals and its area are highly useful in the fields of design, agriculture, and architecture. The concept is highly useful in the advanced designing of navigation maps scaled to actual distances and areas with precision.
The area covered by a quadrilateral formed by joining four different places on a map
To find the area of a quadrilateral, divide it into two triangles using a diagonal. Then calculate the area of each triangle and add them up.
Area of the Quadrilateral = (1/2) × d × (h1 + h2). Here, d = diagonal of the quadrilateral, h1, h2 = heights of the triangles created on either side of the diagonal (d)
The unit of area of a quadrilateral is the same as other shapes, that is, square units of length (square meter, square inches, etc.)
These are the formulas to find the area of special quadrilaterals: - Area of a Square = side × side - Area of a Rectangle = length × width - Area of a Parallelogram = base × height - Area of a Trapezoid = 1/2 × (base1 + base2) × height - Area of a Rhombus = 1/2 × diagonal1 × diagonal2 - Area of a Kite = 1/2 × diagonal1 × diagonal2