To find the area of a trapezoid, you can use the formula:
Area = (base1 + base2) * height / 2
where base1 and base2 are the lengths of the two parallel sides of the trapezoid, and height is the perpendicular distance between the two bases.
In this case, we are given that the length of the trapezoid is 12 inches and 5 inches, and the width is 4 inches. Since the width is not the height of the trapezoid, we need to find the height before we can calculate the area.
To find the height, we can use the Pythagorean theorem, since the trapezoid is a right trapezoid (i.e., one of its angles is a right angle). The height will be the shorter leg of the right triangle, and the longer leg will be the difference between the lengths of the two parallel sides:
height^2 + (base2 - base1/2)^2 = width^2
height^2 + (5-12/2)^2 = 4^2
height^2 + (-1.5)^2 = 16
height^2 = 16 + 2.25
height^2 = 18.25
height ≈ 4.27 inches (rounded to two decimal places)
Now that we have the height, we can plug in the values for the bases and height into the formula for the area:
Area = (base1 + base2) * height / 2
= (12 + 5) * 4.27 / 2
= 62.79 square inches
Therefore, the area of the trapezoid is approximately 62.79 square inches.