Problem
Diagonal AC splits the trapezoid into triangles ABC and ACD, so its area is those two added.
Cutting a hard polygon along a diagonal turns it into triangles, and triangle area is something we already know how to find.
6.G.A.1Identify SubproblemsTaking AC = 20 cm as the base with height 6 cm gives triangle ABC an area of 60.
The 6 cm height is drawn straight to AC, so AC is the natural base to pair it with.
6.G.A.1Draw A DiagramMeasured off base AB = 10 cm instead, that same 60 gives height BC = 12 cm.
Choosing a different base for the same triangle does not change its area, so we can work backward to the unknown side.
6.G.A.1Draw A DiagramTriangle ABC has the same area whichever of its sides is taken as the base.
Half of base times matching height measures the surface the triangle covers, and that surface is one and the same no matter which side we choose to describe it by.
For either choice the triangle is exactly half of the rectangle built on that base and height, so both rectangles hold the very same triangle twice over.
The two ways of computing therefore have to land on the same number, and that is what lets a known area pin down an unknown height.
Base DC = 16 cm with that height 12 cm gives triangle ACD an area of 96.
BC is the horizontal distance from A across to the side DC, so it is exactly the height that goes with base DC.
6.G.A.1Draw A DiagramThe trapezoid's area is the sum of the two triangles.
Putting the two pieces back together rebuilds the whole trapezoid.
6.G.A.1Identify SubproblemsA triangle's area stays the same whichever side you call the base, so pick the base that makes the height easy to use.