The adjacent sides of a parallelogram measure 8 cm and 12 cm and one angle measures 60 degrees. Find the area of the parellelogram.
area=aXb (a cross b in vectors)
area=96*sin60 cm^2
Alright, let's solve this! Now, the area of a parallelogram can be found by multiplying the lengths of any two adjacent sides by the sine of the included angle. In this case, we have sides that measure 8 cm and 12 cm, and an angle of 60 degrees. The formula gives us:
Area = 8 cm * 12 cm * sin(60 degrees)
Now, let's get the value of sin(60 degrees). Oops, sorry my calculator seems to be malfunctioning. Maybe I can ask it to do a funny dance instead. Wait for it... Shake, shake, shake! Okay, that didn't work, but trust me, the value of sin(60 degrees) is √3/2.
So, plugging that into our formula, we have:
Area = 8 cm * 12 cm * (√3/2)
Calculating that out, we get:
Area = 96 cm² * (√3/2)
Now, I don't know about you, but I can't find the square root of 3 in my bag of clown tricks, so I'll just leave it as (√3/2). But don't worry, you can always use a calculator to get an approximate value.
So, the final answer to the area of the parallelogram is 96 cm² * (√3/2).
To find the area of the parallelogram, we can use the formula: Area = base × height. In this case, the base is one of the adjacent sides, and the height is the perpendicular distance between the base and its opposite side.
Given that the adjacent sides of the parallelogram measure 8 cm and 12 cm, let's label these sides as a = 8 cm and b = 12 cm.
Now, we need to find the height of the parallelogram. Since one angle of the parallelogram measures 60 degrees, we can use the trigonometric ratios to find the height.
Let's use the sine function, as sine is the ratio of the opposite side to the hypotenuse in a right triangle. Here, the opposite side is the height of the parallelogram, and the hypotenuse is the longer adjacent side (12 cm).
We have:
sin(60 degrees) = height / 12 cm
To find the height, we can rearrange the equation as:
height = sin(60 degrees) × 12 cm
Using a scientific calculator, we find that sin(60 degrees) is equal to 0.866.
Now, substitute this value into our equation:
height = 0.866 × 12 cm
height ≈ 10.392 cm (rounded to three decimal places)
Finally, we can calculate the area of the parallelogram by multiplying the base and the height:
Area = 8 cm × 10.392 cm
Area ≈ 83.136 cm^2 (rounded to three decimal places)
Therefore, the area of the parallelogram is approximately 83.136 square centimeters.
can you please help me with another problem
Area of parallelogram = bh
A = 8cm X 12cm
A = 96cm2