Two rhombuses have sides with lengths of $16$ $16$ . If one rhombus has a corner with an angle of $\frac{π}{12}$ $pi/12$ and the other has a corner with an angle of $\frac{5 π}{6}$ $(5pi)/6$ , what is the difference between the areas of the rhombuses?

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Two rhombuses have sides with lengths of $16$ $16$ . If one rhombus has a corner with an angle of $\frac{π}{12}$ $pi/12$ and the other has a corner with an angle of $\frac{5 π}{6}$ $(5pi)/6$ , what is the difference between the areas of the rhombuses?

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Answer 1 · 2016-03-20T06:25:59

Difference between the areas of the rhombuses is $30.848$ $30.848$ sq.units.

Explanation:

Area of a parallelogram with sides $a$ $a$ and $b$ $b$ and included angle $θ$ $theta$ is given by $\frac{1}{2} \times a \times b \times sin θ$ $1/2xxaxxbxxsintheta$ . As it is a rhombus, two sides are equal area will be $\frac{1}{2} \times a^{2} \times sin θ$ $1/2xxa^2xxsintheta$ .

Hence area of rhombus with side $16$ $16$ and angle $\frac{π}{12}$ $pi/12$ is

$\frac{1}{2} \times 16^{2} \times sin (\frac{π}{12}) = \frac{1}{2} \times 256 \times 0.259 = 33.152$ $1/2xx16^2xxsin(pi/12)=1/2xx256xx0.259=33.152$

Hence area of rhombus with side $16$ $16$ and angle $5 \frac{π}{6}$ $5pi/6$ is

$\frac{1}{2} \times 16^{2} \times sin (5 \frac{π}{6}) = \frac{1}{2} \times 256 \times 0.5 = 64$ $1/2xx16^2xxsin(5pi/6)=1/2xx256xx0.5=64$

Difference between the areas of the rhombuses is $64 - 33.152 = 30.848$ $64-33.152=30.848$

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Two rhombuses have sides with lengths of $16$ $16$ . If one rhombus has a corner with an angle of $\frac{π}{12}$ $pi/12$ and the other has a corner with an angle of $\frac{5 π}{6}$ $(5pi)/6$ , what is the difference between the areas of the rhombuses?

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Explanation:

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Two rhombuses have sides with lengths of 1616 . If one rhombus has a corner with an angle of π12pi/12 and the other has a corner with an angle of 5π6(5pi)/6 , what is the difference between the areas of the rhombuses?

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Explanation:

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Two rhombuses have sides with lengths of $16$ $16$ . If one rhombus has a corner with an angle of $\frac{π}{12}$ $pi/12$ and the other has a corner with an angle of $\frac{5 π}{6}$ $(5pi)/6$ , what is the difference between the areas of the rhombuses?