Trapazoid with parallel sides left and right. Left labeled 12 inches and right side labeled 10 inches. 2 perpendicular dotted lines at the top and bottom are drawn from left to right top and bottom. What is the area of the quadrilaterals
To find the area of the trapezoid, we first need to find the height of the trapezoid.
Since the two dotted lines are perpendicular to the parallel sides and form right angles, they divide the trapezoid into two right triangles. The height of the trapezoid will be the hypotenuse of one of these right triangles.
Using the Pythagorean theorem, we can find the height:
h^2 + 6^2 = 12^2
h^2 = 144 - 36
h^2 = 108
h = √108
h ≈ 10.39 inches
Now that we have the height, we can find the area of the trapezoid using the formula:
Area = (1/2) * (b1 + b2) * h
Area = (1/2) * (12 + 10) * 10.39
Area = (1/2) * 22 * 10.39
Area ≈ 114.29 square inches
Therefore, the area of the trapezoid is approximately 114.29 square inches.