If x = 4 units, y = 5 units, and h = 6 units, find the area of the trapezoid shown above using decomposition. 39 square units 24 square units 84 square units 54 square units
To find the area of the trapezoid, we first need to find the height of the trapezoid.
Using the Pythagorean theorem, we can find the height by considering the right triangle formed within the trapezoid.
The hypotenuse of the right triangle is h = 6 units
One side is x = 4 units
Let the other side be z
According to the Pythagorean theorem,
6^2 = 4^2 + z^2
36 = 16 + z^2
20 = z^2
z = √20 = 2√5
Now that we have the height of the trapezoid, we can calculate the area using the formula:
Area = 1/2 * (sum of the bases) * height
Area = 1/2 * (4 + 5) * 2√5
Area = 1/2 * 9 * 2√5
Area = 9√5
Therefore, the area of the trapezoid is 9√5 square units.