What is Area of a Quadrilateral?
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.
Measuring the area of a quadrilateral
Calculating the area of a quadrilateral
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)
Area of a parallelogram
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
Area of a rhombus
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
Area of a square
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.
Area of a rectangle
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:
- Area (ABCD) = AB x BC
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