Find the area of a parallelogram with sides of 6 and 12 and an angle of 60°.
To find the area of a parallelogram, you can use the formula: Area = base x height.
In this case, the base of the parallelogram is 12, and the height can be found using trigonometry. Since you have an angle of 60°, the height can be found using the sine function.
First, we need to find the length of the altitude, which is the height of the parallelogram. We can do this by using the sine function:
sin(60°) = opposite / hypotenuse
Let's consider the side with length 6 as the hypotenuse, and the opposite side will be the height (altitude). Therefore, we can write the equation as:
sin(60°) = height / 6
Rearranging the equation gives us:
height = 6 x sin(60°)
Using a calculator:
height ≈ 6 x 0.866 = 5.196
Now that we have the height, we can find the area of the parallelogram:
Area = base x height
Area = 12 x 5.196
Area ≈ 62.352
Therefore, the area of the parallelogram is approximately 62.352 square units.
To find the area of a parallelogram, we can use the formula:
Area = base * height
In this case, the base of the parallelogram is one of its sides, which has a length of 6. The height of the parallelogram is the perpendicular distance between the base and the opposite side.
To find the height, we need to use trigonometry. Since we know one angle of the parallelogram (60°) and the length of one side (12), we can use the sine function to find the height.
The sine of an angle is equal to the ratio of the opposite side to the hypotenuse in a right triangle. In this case, the opposite side is the height of the parallelogram, and the hypotenuse is the side of length 12.
So, we set up the equation:
sin(60°) = height / 12
To solve for the height, we can rearrange the equation:
height = 12 * sin(60°)
Using a calculator, we find that sin(60°) is equal to √3 / 2:
height = 12 * (√3 / 2)
Simplifying further:
height = 6√3
Now that we have the base (6) and the height (6√3), we can calculate the area of the parallelogram:
Area = base * height
= 6 * 6√3
= 36√3
Therefore, the area of the parallelogram is 36√3 square units.