Heron's Formula ( Part - 4 )

1. A rhombus shaped field have green grass for 9 cows to graze . If the each side of the rhombus is 15 m and its longer diagonal is 24 m . How much area of grass field will each cow be getting ?

Sol. Join the diagonal of quadrilateral ABCD

The sides of triangle ABC are

a = 15 m b = 15 m c = 24 m

so , semi perimeter of triangle

S = ( a + b + c ) / 2

S = ( 15 + 15 + 24 ) / 2

S = 54 / 2

S = 27 m

Area of triangle = √ s ( s – a ) ( s – b ) ( s – c )

Area of triangle = √ 27 ( 27 – 15 ) ( 27 – 15 ) ( 27 – 24 )

Area of triangle = √ 3 * 3 * 3 * 12 * 12 * 3

Area of triangle = √ 3 * 3 * 3 * 2 * 2 * 3 * 2 * 2 * 3 * 3

Area of triangle = 2 * 2 * 3 * 3 * 3

Area of triangle = 108 m ^ 2

Area of quadrilateral ABCD = 2 * Area of triangle

Area of quadrilateral ABCD = 2 * 108

Area of quadrilateral ABCD = 216 m^2

The area grazed by cow = total area / number of cows

The area grazed by cow = 216 / 9

The area grazed by cow = 24 m^2

maths ncert solution

2. A rhombus shaped field have green grass for 18 cows to graze . If the each side of the rhombus is 15 m and its longer diagonal is 24 m . How much area of grass field will each cow be getting ?