Answer:
[tex]Area =55.4ft^2[/tex]
Step-by-step explanation:
Given
The attached rhombus
Required
The area
First, calculate the length of half the vertical diagonal (x).
Length x is represented as the adjacent to 60 degrees
So, we have:
[tex]\tan(60) = \frac{4\sqrt 3}{x}[/tex]
Solve for x
[tex]x = \frac{4\sqrt 3}{\tan(60)}[/tex]
[tex]\tan(60) = \sqrt 3[/tex]
So:
[tex]x = \frac{4\sqrt 3}{\sqrt 3}[/tex]
[tex]x = 4[/tex]
At this point, we have established that the rhombus is made up 4 triangles of the following dimensions
[tex]Base = 4\sqrt 3[/tex]
[tex]Height = 4[/tex]
So, the area of the rhombus is 4 times the area of 1 triangle
[tex]Area = 4 * \frac{1}{2} * Base * Height[/tex]
[tex]Area = 4 * \frac{1}{2} * 4\sqrt 3 * 4[/tex]
[tex]Area =2 * 4\sqrt 3 * 4[/tex]
[tex]Area =55.4ft^2[/tex]
