Problem
HGCD is a square with DC = 6 cm, so every side is 6: the height HG and the top piece HD alike.
A square has four equal sides, so knowing one side (6 cm) instantly gives every other side, including the height and the leftover top piece.
4.G.A.2Identify SubproblemsPoint H sits on the top side AD, splitting it into AH and HD. Add the two pieces to get the whole top side.
The top side is just the two labeled chunks placed end to end, so I simply add their lengths.
4.G.A.2Draw A DiagramWith parallel sides 14 and 20 and height 6, the area is (14 + 20) x 6 divided by 2 = 102.
A trapezoid is half of a parallelogram built from the two parallel sides, so averaging them and multiplying by the height gives the area.
6.G.A.1Identify SubproblemsA trapezoid's area is half of its two parallel sides added together, times its height.
Two copies of the trapezoid, one of them turned a half turn, fit together into a parallelogram whose base is the two parallel sides laid end to end.
That parallelogram holds the trapezoid exactly twice over, so one trapezoid is half of it.
Find the hidden side lengths from the square first, then the trapezoid area is just the two parallel sides added, times the height, halved.