Final answer:
To find the area of the region bounded by the isosceles trapezoid ABCD, divide it into a rectangle and two right triangles. Find the height using the Pythagorean theorem, then calculate the area of the trapezoid.
Step-by-step explanation:
To find the area of the region bounded by the isosceles trapezoid ABCD, we need to divide it into a rectangle and two right triangles. Since AB is parallel to CD and the trapezoid is isosceles, we know that AD is also equal to 10 units. Let's start by finding the height of the trapezoid. The height can be found by drawing a perpendicular line from one of the vertices of the trapezoid to the base. This perpendicular line divides the trapezoid into two congruent triangles. Using the Pythagorean theorem, we can find the height:
h^2 = AD^2 - AB^2 = 10^2 - 6^2 = 64
h = √64 = 8 units
Now, we can calculate the area of the trapezoid:
Area = (AB + CD) * h / 2 = (10 + 6) * 8 / 2 = 16 * 8 / 2 = 64 square units