Find the area of the parallelogram.
(base(s)=10cm, slant/side length(s)=6cm, h=? and the angle measure is 60degrees.
a.)15√3 cm^2
b.)30√3 cm^2
c.)15√2 cm^2
I think it's 30√3 cm^2.
To find the area of a parallelogram, we can use the formula A = base × height, where the base is one of the sides of the parallelogram and the height is the perpendicular distance between the base and the opposite side.
In this case, the base of the parallelogram is 10 cm and the slant/side length is 6 cm. We need to find the height.
Since we know the angle measure is 60 degrees, we can see that the height is equal to the side length multiplied by the sine of the angle.
Using the formula: height = side length × sin(angle),
height = 6 cm × sin(60 degrees) = 6 cm × √3/2 = 3√3 cm.
Now we can calculate the area using the formula:
A = base × height = 10 cm × 3√3 cm = 30√3 cm².
Therefore, the area of the parallelogram is 30√3 cm², which corresponds to option b.
To find the area of a parallelogram, you can use the formula:
Area = base × height
In this case, you are given the base of 10 cm and the side length (slant) of 6 cm. However, you need to determine the height of the parallelogram.
Since you are given the angle measure of 60 degrees, you can use trigonometry to find the height. In a parallelogram, the height is the perpendicular distance between the base and the opposite side.
To find the height, you can use the formula:
height = slant × sin(angle)
In this case, plugging in the values you have:
height = 6 cm × sin(60 degrees)
Using a scientific calculator or reference tables, you can find that sin(60 degrees) = √3/2. Substituting this back into the formula:
height = 6 cm × √3/2
Now you can calculate the height:
height = 3√3 cm
Finally, you can substitute the values of base and height into the area formula:
Area = 10 cm × 3√3 cm
Calculating this, you get:
Area = 30√3 cm^2
So, you are correct. The area of the parallelogram is 30√3 cm^2.