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Chapter 5: Problem 16

Find the area of a parallelogram that has pairs of sides of lengths 3 and \(12,\) with a \(\frac{\pi}{3}\) radian angle between two of those sides.

Short Answer

Expert verified
The area of the parallelogram with given sides and angle is \(18\sqrt{3}\) square units.

Step by step solution

01

Identify the given values

Length of side 1: 3 units Length of side 2: 12 units Angle between the sides: \(\frac{\pi}{3}\) radians
02

Write down the formula for the area of a parallelogram

Area = side1 * side2 * sin(angleBetweenSides)
03

Plug the given values into the formula

Area = 3 * 12 * sin(\(\frac{\pi}{3}\))
04

Calculate the sine of the angle

Since we know that sin(\(\frac{\pi}{3}\)) is equal to \(\frac{\sqrt{3}}{2}\), we can substitute it in the formula: Area = 3 * 12 * \(\frac{\sqrt{3}}{2}\)
05

Calculate the area

Area = 3 * 12 * \(\frac{\sqrt{3}}{2}\) = 36 * \(\frac{\sqrt{3}}{2}\) = \(18\sqrt{3}\) square units Thus, the area of the parallelogram is \(18\sqrt{3}\) square units.

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Most popular questions from this chapter

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