To find the perimeter, add the four side lengths. To find the area, calculate the product of the base and the height.
Perimeter: 174.4m Area: 1520m^2
Practice makes perfect
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 one side length of the parallelogram is 40 meters, 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 meters.
Now, note that one of the sides whose length is missing is the hypotenuse of the right triangle formed at below the diagram.
For this right triangle, the lengths of the legs are 38 meters and 28 meters. 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 approximately 47.2 meters. This is also the length of a side of the parallelogram. Therefore, the length of its opposite side is also approximately 47.2 meters.
Now we can add the four side lengths to obtain the perimeter. Because we are using approximated values of two sides, the perimeter is also an approximation.
Perimeter: 40+47.2+40+47.2=174.4
The perimeter of the parallelogram to the nearest tenth is 174.4m.
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 meters as the base and its corresponding height which is 38 meters.
We can substitute these two values into the formula for the area of a parallelogram and simplify.
