find the area of a parallelogram with diagonals of lengths 10 inches and 22 inches that intersect at a 65 degrees angle
To find the area of a parallelogram with diagonals of lengths 10 inches and 22 inches that intersect at a 65 degree angle, you can use the formula:
Area = 0.5 * d1 * d2 * sin(angle)
where d1 and d2 are the lengths of the diagonals, and angle is the angle between the diagonals.
Step 1: Write down the given values:
d1 = 10 inches
d2 = 22 inches
angle = 65 degrees
Step 2: Convert the angle to radians:
angle_radians = angle * π/180
Step 3: Use the formula to calculate the area:
Area = 0.5 * d1 * d2 * sin(angle_radians)
Area = 0.5 * 10 inches * 22 inches * sin(65 degrees * π/180)
Step 4: Calculate the sine of the angle:
sin(65 degrees * π/180) ≈ 0.9063
Area = 0.5 * 10 inches * 22 inches * 0.9063
Step 5: Perform the multiplication and simplify:
Area ≈ 99.843 square inches
Therefore, the area of the parallelogram is approximately 99.843 square inches.