Question

Find the area of following rhombuses. Round your answers to the nearest tenth if
necessary.

Answer 1

`Area =55.4ft^2`

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:

`\tan(60) = (4\sqrt 3)/(x)`

Solve for x

`x = (4\sqrt 3)/(\tan(60))`

`\tan(60) = \sqrt 3`

So:

`x = (4\sqrt 3)/(\sqrt 3)`

`x = 4`

At this point, we have established that the rhombus is made up 4 triangles of the following dimensions

`Base = 4\sqrt 3`

`Height = 4`

So, the area of the rhombus is 4 times the area of 1 triangle

`Area = 4 * (1)/(2) * Base * Height`

`Area = 4 * (1)/(2) * 4\sqrt 3 * 4`

`Area =2 * 4\sqrt 3 * 4`

`Area =55.4ft^2`