Parallelogram WXYZ is a plane figure with four sides, opposite sides parallel and congruent, and opposite angles congruent as well. To calculate the perimeter of parallelogram WXYZ, we need to understand what perimeter is first.
Perimeter is the total distance around the outside edge of any two-dimensional shape. It’s like measuring the length of a string that surrounds the shape. To find the perimeter of parallelogram WXYZ, we need to add the length of all four sides together.
Assuming we know the measurements of each side of parallelogram WXYZ, we can use the formula P = 2(L + W), where P is perimeter, L is the length, and W is the width.
However, in most cases, the perimeter of a parallelogram is not given directly. We need to find it by calculating the sum of the four sides of the parallelogram, which could be different lengths. For example, if we know that the length of the sides WX and YZ are 5 units and 7 units, respectively, and the length of the height from base WZ is 3 units, we can find the length of the remaining sides.
First, we can use the Pythagorean theorem to calculate the length of side WY, which will give us the final length of the parallelogram WXYZ. The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
To apply this theorem, we need to divide parallelogram WXYZ into two right-angled triangles. We can do this by drawing a line from point X perpendicular to side WZ. Let’s call the point where the line intersects WZ point M.
Now, we have two right-angled triangles, WMX and YMZ. We know that the height of parallelogram WXYZ is 3 units, which is also the length of line segment XM. By subtracting XM from WX (5 units), we get the length of line segment MW, which is 4 units.
Next, we can calculate the length of line segment WY using the Pythagorean theorem. The length of WY is the hypotenuse of triangle WMX, and the side lengths are 4 units and the height of parallelogram WXYZ, which is 3 units. So, the length of WY is the square root of 4 squared plus 3 squared, which is the square root of 16 + 9, or √25, which equals 5 units.
Finally, we can calculate the perimeter of parallelogram WXYZ by adding the length of all four sides together, which is 5 + 5 + 7 + 4, or 21 units.
In conclusion, the perimeter of parallelogram WXYZ is 21 units, assuming that the length of the sides WX and YZ are 5 units and 7 units, respectively, and the length of the height from base WZ is 3 units. We can use the formula P = 2(L + W) to calculate the perimeter when the length and width are given, or we can use the Pythagorean theorem to find the length of the remaining sides if only some side lengths and the height are given.