Chapter 10.3, Problem 34E

To determine

To calculate the area.

Answer to Problem 34E

  $n^{2}2\sqrt{3}$

Explanation of Solution

Given Information: Side of equilateral triangle = 2n and 1 angle is of 30°

Formula Used:Area of Rhombus = $Base\times Height$ , $\tan \theta =\frac{Perpendicular}{Height}$

Calculation:

Draw the equilateral triangle into 2 right-angled triangle.

So,

Perpendicular = $\frac{Base}{2}=\frac{2n}{2}=n$

Now, find the Height.

  $\tan \theta =\frac{Perpendicular}{Height}$

After put the value of $\tan \theta$ and $Perpendicular$

  $Height=\frac{Perpendicular}{\tan \theta }$

  $Height=\frac{n}{\tan 30°}$

  $\tan 30°=\frac{1}{\sqrt{3}}$

So,

  $Height=\frac{n}{\frac{1}{\sqrt{3}}}$

  $Height=n\sqrt{3}$

Now, find Area of Rhombus by putting value of Base and Height.

  $Base=2n$ and $Height=n\sqrt{3}$

Area of Rhombus = $Base\times Height$

Area of Rhombus = $2n\times n\sqrt{3}$

Area of Rhombus = $n^{2}2\sqrt{3}$