Question

Find the
area of the rhombus.

Answer 1

`\large\boxed{A=32\sqrt3\ m^2}`

Explanation:

`\bold{METHOD\ 1:}\\\\\text{We have four right triangles with legs}\ a=4\sqrt3\ m,\ b=4m.\\\\\text{The formula of an area of a right triangle}:\\\\A=(ab)/(2)\\\\\text{Substitute:}\\\\A_\triangle=((4\sqrt3)(4))/(2)=(16\sqrt3)/(2)=8\sqrt3\ m^2\\\\\text{The area of the rhombus}\\\\A=4A_\triangle\to A=(4)(8\sqrt3)=32\sqrt3\ m^2`

`\bold{METHOD\ 2:}\\\\\text{The formula of an area of a rhombus:}\\\\A=(ef)/(2)\\\\e,\ f-\text{diagonals}\\\\\text{We have}\\\\e=(2)(4)=8\ m\\f=(2)(4\sqrt3)=8\sqrt3\ m\\\\\text{Substitute:}\\\\A=((8)(8\sqrt3))/(2)=(64\sqrt3)/(2)=32\sqrt3\ m^2`