A parallelogram is a quadrilateral where both of the pairs of opposite sides are parallel and congruent. Any side can be called the base of the parallelogram. Its height is the perpendicular distance between any two parallel bases. For the given parallelogram, we will find its perimeter and area one at a time.
Perimeter
The perimeter of a parallelogram is calculated by adding its four side lengths.
We are given that lengths of two adjacent sides of the parallelogram are 21 feet and 17 feet, but we are missing the two other measurements. However, the opposite sides of parallelograms are congruent, so we know that their lengths are also 21 feet and 17 feet.
Now we can add the four side lengths to obtain the perimeter.
Perimeter: 21+17+21+17=76 ft
Area
The area of a parallelogram is the product of a base and its corresponding height. We can consider the side whose length is 21 feet as the base. However, we need to find the height. To do so, we will pay close attention to the right triangle formed on the right-hand side of the figure.
For this right triangle, the length of one leg is 8 feet and the length of the hypotenuse is 17 feet. Let's substitute these values into the Pythagorean Theorem and solve for the leg h.
Note that we only kept the principal root when solving the equation, because h is the leg of a right triangle and it must be non-negative. The length of the leg is 15 feet. This is also the length of the height of the parallelogram.
Now we can substitute lengths of the base and the height into the formula for the area of a parallelogram and simplify.
