Problem
B is the midpoint of the right side and D is the midpoint of the left side. The segment BD runs straight across the middle of the outer square, so its length equals the outer square's side, 16 cm.
Connecting opposite side-midpoints of a square gives a segment as long as the side itself.
4.G.A.2Draw A DiagramSegment BD, joining the midpoint of the outer square's left side to the midpoint of its right side, is exactly as long as one side of the outer square.
B and D sit at the same height, so BD lies flat across the square and, together with the square's bottom side, forms the top and bottom of a rectangle.
The top and bottom of a rectangle are opposite sides, and folding the rectangle along the line halfway between them drops BD exactly onto the bottom side, matching them length for length.
The diagonals of the inner square bisect each other at center M, so M is the midpoint of BD. Therefore BM = BD / 2 = 16 / 2 = 8 cm.
A square's diagonals cut each other exactly in half, so BM is half of 16 cm.
4.G.A.2Identify SubproblemsJoining opposite side-midpoints of a square gives a line as long as the side, and the diagonals split in half -- so BM is just 16 divided by 2!