Find the area of a parallelogram with sides of length 6 and 8, and with an interior angle with measure 45 degrees.
*Solved
what is it?
To find the area of a parallelogram, we can use the formula: Area = (base * height).
In this case, the base and height need to be determined.
Step 1: Determine the base.
The base of a parallelogram is typically one of the sides. Therefore, in this case, we can use either side length of 6 or 8 as the base.
Step 2: Determine the height.
The height of a parallelogram is the perpendicular distance between the base and its opposite side.
To find the height, we need to determine the length of the perpendicular from one of the vertices to the opposite side.
To do this, we can use trigonometry, specifically the sine function, since we have the length of one side and the angle between that side and the perpendicular.
Using the given angle of 45 degrees, we can solve for the height:
sin(45) = height / 6 (or 8) => height = 6 * sin(45) (or 8 * sin(45)).
Step 3: Calculate the area.
Now that we have the base and the height, we can use the formula: Area = (base * height).
Therefore, the area of the parallelogram can be calculated as:
Area = (6 * 6 * sin(45)) = 18 square units (if the base is 6)
Or
Area = (8 * 8 * sin(45)) = 32 square units (if the base is 8).