As we have learnt in earlier classes about figures of different shapes such as squares, rectangles, triangles and quadrilaterals. Also calculated perimeters and the areas of some of these figures like rectangle, square etc.
Unit of measurement for length or breadth is taken as metre (m) or centimeter (cm) etc.
Unit of measurement for area of any plane figure is taken as square metre (m2) or square centimetre (cm2) etc.
Area of a triangle = 1/2 x base x height
Area of a Triangle — by Heron's Formula
Heron was born in about 10AD possibly in Alexandria in Egypt. He worked in applied mathematics. His works on mathematical and physical subjects are so numerous and varied that he is considered to be an encyclopedic writer in these fields. His geometrical works deal largely with problems on mensuration written in three books.
Book I deals with the area of squares, rectangles, triangles, trapezoids (trapezia), various other specialized quadrilaterals, the regular polygons, circles, surfaces of cylinders, cones, spheres etc. In this book, Heron has derived the famous formula for the area of a triangle in terms of its three sides.
Area of a triangle = √s(s-a)(s-b)(s-c)
Where a, b and c are the sides of the triangle, and s = semi-perimeter, i.e., half the perimeter of the triangle =a + b + c/2.
Let's there is a farmer has a land to be cultivated and she employs some labourers for this purpose on the terms of wages calculated by area cultivated per square metre.
To find the solution we need to divide the quadrilateral in triangular parts and then use the formula for area of the triangle and so on.