Question

What is the area of the trapezoid? The diagram is not drawn to scale.

Answer 1

I am redrawing the figure and relabelling it so that I can reference it:

Answer 2

EC measures 6 cm , because you have a trapezoid and the this just represents the height. BC measures 8 because BCEF is just a rectangle



Now, what is the measure of AB? Well, triangle CDE and ABF are actually congruent by the side-angle-angle theorem. They have 2 same corresponding angles, and then the side is 6 cm for both triangles. Hence, AB measures 4 cm, just like CD

So, the formula for the area of a trapezoid is \[\text{Area}=\frac{b+B}{2}\cdot h \], where \(b\) is the small base, which is EF = 8 cm here. \(B\) is the large base, which is AD which measures 4+8+4 cm = 16 cm

The height is the measure BF = 6 cm.

Hence, \[\text{Area}=\frac{8+16}{2}\cdot 6=72 \text{ cm}^2 \]