Quadrilateral area=S, find area of triangle in terms of S?

Question

In quadrilateral ABCD, lines AD and BC are parallel. M is the midpoint of AB. S is the area of ABCD. Find the area of triangle DMC in terms of S.

Answer 1

Area of a qudralateral is:

Area = (1/2)(AD+BC)h. where h is the perpendicular distance between the sides AD and BC

Area of DMC is (1/2)h1*BC + (1/2)h2*AD

But h1 is the altitude of the triangle BCM and it is parallel to h and equal to h/2 and likewise for h2 using the AMD triangle. It is easier to see if you draw out the problem. So:

h1 = h2 = h/2 so:
Area of DMC = (1/4)h(BC + AD)

Therefore the area of DMC is S/2

Answer 2

nicely you gave teh equation wiuth the knowns of teh top and the backside it truly is a surprisingly straightforward plug and chug A = a million/2 *Base * hieght A= a million/2 * 20 m * 22 m Plug and chug A= 220 m ^2