The perimeter of a parallelogram is calculated by adding its four side lengths.
We are given that one side length of the parallelogram is 40 inches, but we are missing the other three measurements. However, the opposite sides of parallelograms are congruent, so we know that the length of the opposite side is also 40 inches.
Now, note that one of the sides whose length is missing is the hypotenuse of the right triangle formed on the left of the diagram.
For this right triangle, the lengths of the legs are 36 inches and 27 inches. Let's substitute these values into the Pythagorean Theorem and solve for the hypotenuse c.
Note that we only kept the principal root when solving the equation because c is the hypotenuse of a right triangle and it must be non-negative. The length of the hypotenuse is 45 inches. This is also the length of a side of the parallelogram. Therefore, the length of its opposite side is also 45 inches.
Now we can add the four side lengths to obtain the perimeter.
Perimeter: 40+45+40+45=170in.
Area
The area of a parallelogram is the product of its base and its height. In the given parallelogram, we can consider the side whose length is 40 inches at the base and its corresponding height is 36 inches.
We can substitute these two values into the formula for the area of a parallelogram and simplify.
