A parallelogram has sides A, B, C, and D. Sides A and B have a length of $5$ $5$ and sides C and D have a length of $4$ $4$ . If the angle between sides A and C is $\frac{5 π}{8}$ $(5 pi)/8$ , what is the area of the parallelogram?

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A parallelogram has sides A, B, C, and D. Sides A and B have a length of $5$ $5$ and sides C and D have a length of $4$ $4$ . If the angle between sides A and C is $\frac{5 π}{8}$ $(5 pi)/8$ , what is the area of the parallelogram?

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Answer 1 · 2016-02-27T10:36:11

$4 \cdot 5 \cdot sin (\frac{5 π}{8}) \approx 18.48$ $4*5*sin((5pi)/8) ~~18.48$

Explanation:

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The area of a paralllogram is given by the formula $\frac{1}{2} \cdot B a s e \cdot H e i g h t$ $1/2*Base*Height$

We therefore need to calculate the height $h$ $h$ of the paralleogram.
$sin (\frac{5 π}{8}) = \frac{h}{A}$ $sin((5pi)/8) = h/A$
$:.h = Asin((5pi)/8) = 5sin((5pi)/8)$

The base is $C$ which is given as $4$

The area is $4*5sin((5pi)/8) ~~18.48$

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A parallelogram has sides A, B, C, and D. Sides A and B have a length of $5$ $5$ and sides C and D have a length of $4$ $4$ . If the angle between sides A and C is $\frac{5 π}{8}$ $(5 pi)/8$ , what is the area of the parallelogram?

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A parallelogram has sides A, B, C, and D. Sides A and B have a length of 5 55 and sides C and D have a length of 4 4 4 . If the angle between sides A and C is (5 pi)/8 5π8(5 pi)/8 , what is the area of the parallelogram?

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A parallelogram has sides A, B, C, and D. Sides A and B have a length of $5$ $5$ and sides C and D have a length of $4$ $4$ . If the angle between sides A and C is $\frac{5 π}{8}$ $(5 pi)/8$ , what is the area of the parallelogram?