Remark
This is quite a nice little problem. It takes a minute or three to figure out the answer, and when you do, you will be certain that you have been tricked. It is a little like the egg of Columbus.
Solution
The Base of Triangle ABN is AB
The Base of Triangle CDM is CD
The height of both given triangles is h. That is the distance between the two parallel lines.
Area ABN = 1/2*AB * h = 23 cm^2
Area CDM = 1/2*CD * h = 18 cm^2
Now the Area of the trapezoid is
Area_Trapezoid = 1/2 * h (AB + CD) Using the distributive property Remove the brackets.
Area_Trapezoid = 1/2*AB*h + 1/2*CD*h Did you notice something? Those terms are just the area of the triangles (written above.)
Area Trapezoid = 23 + 18 = 41 cm^2 <<<< Answer
