Problem
The square's side is 10 cm, so its area is side times side.
Area of a square is just side x side, a Grade 4 formula, so this is the easiest piece to nail down first.
4.MD.A.3Identify SubproblemsThe square is 5 times the overlap, so the overlap is the square's area divided by 5.
If 5 copies of the overlap make 100, one copy is 100 split into 5 equal parts.
4.OA.A.3Work BackwardsThe rhombus is 3 times the overlap, so multiply the overlap by 3.
Now that I know one overlap is 20, three of them is just 20 added three times.
4.OA.A.3Identify SubproblemsThe rhombus has an area of 60 square centimeters.
The square is 5 times the overlap, so the overlap is the square's 100 split into 5 equal parts, which is 20.
The rhombus is 3 times that same overlap, so its area is three copies of 20.
Dividing to reach the overlap and then multiplying back up are opposite moves, so nothing is lost passing through the middle step.
The rhombus's vertical diagonal AC lies along the square's side, so AC = 10 cm.
The drawing lines up the diagonal with the square's side, so I can borrow that 10 cm measurement directly.
6.G.A.1Draw A DiagramArea is one diagonal times the other divided by 2, so 10 x BD divided by 2 = 60 gives BD = 12 cm.
Half of (10 x BD) is 60, so 10 x BD is 120, and the diagonal must be 12 cm.
6.G.A.1Work BackwardsWhen you cannot reach the answer directly, solve the easy pieces first and let them carry you to the hard one.