Use the triangle formed by the height of the trapezoid to find the lengths of the two sides of the trapezoid and the length of :

 .   cm.

This finds the base of the triangle, which can be added twice to  to find :  cm.

Now, use the same triangle to find the length of the sides.

 .  cm.

Lastly, add all of the lengths together:  cm.

We can then use the Pythagorean Theorem to find the right portion of the bottom base.  We can then use this value to determine the left portion.

Using Pythagorean Theorem again, we can calculate the left leg to be 20.  That means we now know all four sides.  The perimeter is simply the sum.

To find the perimeter of this trapezoid, first find the length of the larger base. Then, find the sum of all of the sides. It's important to note that since this is an isosceles trapezoid, both of the non-parallel sides will have the same length. 

The solution is:

The smaller base is equal to  inches. Thus, the larger base is equal to:



, where  the length of one of the non-parallel sides of the isosceles trapezoid. 

The measurements that Dr. Robinson gave to the contractor include the lengths of the two base sides and one of the non-parallel sides of the property. Since Dr. Robinson's property is shaped like an isosceles trapezoid, there must be two non-parallel sides of equal length. 

The solution is:

The correct answer is 128 sq ft. 

There are two ways to find the total area.   One way to find the total area, you must find the area of the triangle and rectangle separately.  After some deduction , you can find that the base of the triangle is 6 ft.   Then using the Pythagorean Theorem, or 3-4-5 right triangles, you can find that the height of the triangle and rectangle is 8 ft. 

To find the area of the triangle, you would multiply 6 by 8 and then divide by 2 to get 24.  To find the area of the rectangle, you would multiply 8 by 13 to get 104.  Then you would add both areas to get 128 sq ft. 

The other way to find the area  is to use the formula for area of a trapezoid. After some deduction , you can find that the base of the triangle is 6ft.   Then using the Pythagorean Theorem or 3-4-5 right triangles, you can find that the height of the triangle and rectangle is 8 ft. 

Then you use the formula: 

to get

Start by drawing in the height, , to form a right triangle.

Use the Pythagorean Theorem to find the length of .

Now that we have the height, plug in the given information into the formula to find the area of the trapezoid.

Keep in mind that .

The question asks you to find the length of .

First, draw in the height .

First, find  by using .

Now, plug in the values for area, height, and one base to find the length of the second base, .

First, draw in the height.

First, find the height by using .

Now, plug in the values for area, height, and one base to find the length of the second base, .

First, draw in the height.

First, find the height by using .

Now, plug in the values for area, height, and one base to find the length of the second base, .

The formula to find the area of a trapezoid is

.

Substitute in the values for the area, a base, and the height. Then solve for .