Note that, the trapezoid is composed of the parallelogram and the triangle at the bottom.
The perimeter of a trapezoid is calculated by adding its four side lengths. In our case, one of the sides is divided into two segments.
We are given that one side length of the parallelogram is 39 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 39 inches.
Now, note that one of the sides whose length is missing is the hypotenuse of the right triangle formed on the bottom of the diagram.
For this right triangle, the lengths of the legs are 37 inches and 24 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 about 44.102 inches. This is also the length of a side of the parallelogram. Therefore, the length of its opposite side is also 44.1 inches.
Now we can add the five side lengths to obtain the perimeter.
Perimeter: 39+37+24+39+44.1 = 183.1in.
Area
The area of a trapezoid is half of the product of the sum of its bases and its height. In the given trapezoid, we can see that the measures of the bases are 39 inches and 39+ 24 = 63 inches. The height of the trapezoid is 37 inches.
We can substitute these two values into the formula for the area of a trapezoid and simplify.
