Problem
Draw the rectangle, mark O on side DC, then add the copy you get by turning it a half turn about O.
Fourth graders can recognize and draw a figure that looks the same after a half turn, so sketching the turned copy makes the new outline visible.
4.G.A.3Draw A DiagramEach rectangle is 15 cm by 9 cm, so one rectangle's perimeter is 2 times 15 plus 2 times 9.
Going around a rectangle means two long sides plus two short sides, a perimeter formula a fourth grader uses comfortably.
4.MD.A.3Identify SubproblemsAlong DC the two rectangles share a strip 2 x OC long, and that strip ends up inside the joined figure.
A point-symmetric turn carries C to a point as far past O as C is in front of O, so the touching strip is exactly two OC lengths, and seeing it in the picture shows it sits inside.
4.G.A.3Draw A DiagramEach rectangle gives that strip up, so the perimeter is 48 + 48 less two copies of it.
Perimeter is just the distance around the outside, so any edge that ends up inside is removed from both shapes that shared it.
3.MD.D.8Identify SubproblemsThe finished figure's perimeter is the two rectangle perimeters added, less the shared strip taken off once from each.
The half-turn copy is the same rectangle simply moved, so it has the very same perimeter as the original.
Where the two rectangles meet, each one gives up that shared strip from its own outline, so the strip leaves the boundary once from each side.
The finished perimeter is 84 cm, so 96 minus 4 times OC equals 84. That means 4 times OC equals 12, so OC equals 3.
When you know the total around the outside, you can undo the steps to recover the one missing length.
3.MD.D.8Work BackwardsWhen two copies join along a shared edge, that edge hides inside, so subtract it from both perimeters to find the leftover length.