Find the area of the trapezoid by decomposing it into other shapes

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To find the area of the trapezoid, we can decompose it into a rectangle and two right triangles.

Let's denote the trapezoid as ABCD, where AB and CD are the parallel bases, and AD and BC are the non-parallel sides.

First, let's draw a line from point C perpendicular to AD, creating two right triangles (triangle DCF and triangle ECB) and a rectangle (rectangle ADFC).

Now, we know that the area of a rectangle is given by length x width. In this case, the width is AF (which is the same as CD) and the length is AD. So, the area of the rectangle ADFC is AF x AD.

Next, we know that the area of a triangle is given by 1/2 x base x height. In this case, the base of triangle DCF is FC and the height is AD. So, the area of triangle DCF is 1/2 x FC x AD. Similarly, the area of triangle ECB is 1/2 x EC x AD.

Therefore, the total area of the trapezoid ABCD is the sum of the areas of the rectangle and the two triangles:

Area = (AF x AD) + (1/2 x FC x AD) + (1/2 x EC x AD)

Now, using the measurements of AF, FC, EC, and AD, plug in the values and calculate the area of the trapezoid.