Question

A rhombus shaped field has green grass for 18 cows to gave if each side of the rhombus is 30m and it's longer diagonal is 48 m, what is the area of field​

Answer 1

$\huge\rm\green{༆Question:-}$

• A rhombus shaped field has green grass for 18 cows to gave if each side of the rhombus is 30m and it's longer diagonal is 48 m, what is the area of field

$\huge\rm\red{༆Given:-}$

• ABCD is a rhombus

Here triangles ABC and ADC are congruent,

$ar (∆ABC) = ar (∆ADC)$

Also triangles ABC and ADC have equal perimeters.

$Semi-perimete r \: of \: ∆ABC \: = \: ∆ADC$

$\: \: \: s = \frac{30 + 30 + 48}{2} \\ = \frac{108}{2} \\ = 54 \: cm$

$•Area \: of \: ∆ABC \: = \: Area \: of \: ∆ADC$

$= \sqrt{54(54 - 30)(54 - 30)(54 - 48)}$

$= \sqrt{54 \times 24 \times 24 \times 6} \: \: = \: 432 \: {m}^{2}$

❥︎Therefore,

Area of rhombus ABCD

$= 2 \times \: area \: of \: ∆ABC \\ = 2 \times 432$

$= 864 \: {m}^{2}$

$Also \: area \: o f \: grass \: field .$

$= \frac{864}{18} {m}^{2} \\ \\ = 48 \: {m}^{2}$