A rhombus shaped field has green …

We will divide the given rhombus into two triangles, and by using Heron’s formula, we can calculate the area of triangles. Heron formula for the 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 = Half the Perimeter of the triangle = (a + b + c)/2 A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting Let the longer diagonal AC divides the rhombus ABCD into two congruent triangles. For ∆ABC, a = b = 30 m, c = 48 m And Semi Perimeter(s) = (a + b + c)/2 s = (30 + 30 + 48)/2 s = 108/2 s = 54 m By using Heron’s formula, Area of ΔABC = √s(s - a)(s - b)(s - c) = √54(54 - 30)(54 - 30)(54 - 48) = √54 × 24 × 24 × 6 Area of ΔABC = 432 m2 Area of rhombus = 2 × Area of a ΔABC = 2 × 432 m2 = 864 m2 Since, number of cows = 18 The area of grass field will each cow get = (Total area of the rhombus) / 18 = 864 m2/18 = 48 m2 Thus, each cow will be getting a 48 m2 area of the grass field.