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Question

An isosceles trapezoid ABCD has bases AD = 17 cm, BC = 5cm, and leg AB = 10cm. A line is drawn through vertex B so that it bisects diagonal AC and intersects AD at point M. Find the area of ΔBDM.

 

 

I can't figure out where on line AD point M lies.

Answer 1

One way to locate point M is to use coordinate geometry. See this graph:

 

https://www.desmos.com/calculator/7puz1lavso

 

Using this graph you can see that the coordinates of the midpoint of diagonal AC are (5.5,4). Now write the equation of the line through B and that midpoint. Determine the x value of the point with y coordinate 0 that lies on that line. Turns out to be (5,0). That allows you to determine the length of the base of the target triangle (it is 17 - 5, or 12). The height of the target triangle is 8 (segment BH on the graph). Now you should be able to use A = 1/2 base times height.