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 $3$ $3$ . If the angle between sides A and C is $\frac{π}{3}$ $pi/3$ , 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 $3$ $3$ . If the angle between sides A and C is $\frac{π}{3}$ $pi/3$ , what is the area of the parallelogram?

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Answer 1 · 2016-03-16T23:10:45

$15 \frac{\sqrt{3}}{2}$ $15\sqrt{3}/2$ square units.

Explanation:

The area of a parallelogram is the product of two adjacent sides times the sine of the angle between them.

Hence area is $5 \times 3 \times sin (\frac{π}{3}) = 15 \frac{\sqrt{3}}{2}$ $5xx3xxsin(pi/3)=15sqrt3/2$ square units

(For a given parallelogram, there are two possible values for the angle, but these are supplementary to each other and thus have the same sine. Also $sin (π - θ) = sin θ$ $sin(pi-theta)=sintheta$ )

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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 $3$ $3$ . If the angle between sides A and C is $\frac{π}{3}$ $pi/3$ , 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 55 and sides C and D have a length of 3 3 . If the angle between sides A and C is π3pi/3 , 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 $3$ $3$ . If the angle between sides A and C is $\frac{π}{3}$ $pi/3$ , what is the area of the parallelogram?