find the area of a parallelogram with diagonals of lengths 10 inches and 22 inches that intersect at a 65 degrees angle.
We would have 4 equal triangles
let's look at one of these that contain the 65° angle.
Height/11 = sin65
height = 9.969
area = 4( (1/2)(5)(9.969) = 99.694
that last answer posted is wrong
To find the area of a parallelogram, we need to know either the length of the base and the corresponding height, or the lengths of the diagonals and the angle between them. In this case, we are given the lengths of the diagonals, 10 inches and 22 inches, and the angle between them, 65 degrees.
To find the area, we can use the formula:
Area = 1/2 * d1 * d2 * sin(angle)
where d1 and d2 are the lengths of the diagonals and angle is the angle between them.
First, let's convert the angle from degrees to radians, as many trigonometric functions use radians. To convert degrees to radians, we use the formula:
radians = degrees * π / 180
Substituting the given angle into the formula, we have:
angle_radians = 65 * π / 180
Now, let's substitute the given values into the area formula:
Area = 1/2 * (10 inches) * (22 inches) * sin(65 degrees)
Using a calculator, evaluate the sine of the converted angle. Then, multiply the result by half of the product of the diagonals:
Area = 1/2 * (10 inches) * (22 inches) * sin(angle_radians)
After performing the necessary calculations, you will find the area of the parallelogram.