Does any line through the centroid of a trapezoid divid it into 2 equal halfs?
No, it does not. Here is an intuitive way to approach it. Consider a trapezoid with horizontal bases. Make the top base arbitrarily small. The trapezoid then approaches the shape of a triangle, as near as we please. Now consider a triangle dissected by a horizontal line through its centroid. The top section is a triangle, similar to the original, with a similarity ratio of 2/3. That makes its area 4/9 the original, not 1/2. Followup: My response was to the proposition that striking a line through the centroid was sufficient to dissect the trapezoid into equal areas. After reading dingodevil’s comments, I disagree on a minor point, but agree with his main thrust, that the question was abiguous. Now you have followed it with a more interesting challenge. You want to dissect the trapezoid into equal areas using a line parallel to the bases. Let the trapezoid have bottom base a, top base b, and height h. After the dissection, the lower half has bottom base a and height k. Now find its top
