What is the area of a parallelogram with a 60 degree angle and length of 6cm and side 8cm
area = (6)(8)sin60°
= 48√3/2 = 24√3
To find the area of a parallelogram, we need to multiply the length of the base by the height.
In this case, the base of the parallelogram is the side length of 6 cm.
The height of the parallelogram can be found by drawing an altitude from one of the base angles. Since we know that one angle is 60 degrees and the side opposite that angle is 8 cm, we can use trigonometry to find the height.
Using the formula:
height = side length * sin(angle)
The height is given by:
height = 8 cm * sin(60 degrees)
Now we can calculate the height:
height = 8 cm * (sqrt(3)/2)
height = 8 cm * (1.732/2)
height = 8 cm * 0.866
height = 6.928 cm (rounded to three decimal places)
Finally, we can calculate the area of the parallelogram:
area = base * height
area = 6 cm * 6.928 cm
area = 41.568 cm^2 (rounded to three decimal places)
Therefore, the area of the parallelogram is 41.568 square centimeters.
To find the area of a parallelogram, you need to multiply the length of its base by its corresponding height. In this case, the base of the parallelogram is given as 6 cm. However, we need to calculate the corresponding height.
Since we know the length of one side (8 cm) and the angle opposite to it (60 degrees), we can use trigonometric functions to find the height of the parallelogram.
The height can be calculated using the formula: height = side * sin(angle).
First, convert the angle from degrees to radians. The formula requires angles to be in radians, so we need to convert 60 degrees to radians.
Radians = (π/180) * degrees
Radians = (π/180) * 60
= π/3
To find the height, multiply the side length (8 cm) by the sine of the angle (π/3):
height = 8 cm * sin(π/3)
Now, we can calculate the value:
height = 8 cm * 0.866
≈ 6.9282 cm
Now that we have the base (6 cm) and the height (6.9282 cm), we can calculate the area of the parallelogram using the formula:
Area = base * height
Area = 6 cm * 6.9282 cm
≈ 41.569 cm²
Therefore, the area of the parallelogram is approximately 41.569 square centimeters.