AMC 10 · 2007 · #1
Grade 4 geometry-2dPick an answer.
The total is built from several smaller pieces — the area of one bedroom's four walls, the unpainted doorways/windows, and the fact that there are three bedrooms — so Tool #7 (Identify Subproblems) solves it one layer at a time: one wall, one bedroom, then all three. Tool #1 (Draw a Diagram) keeps the box straight so that only the four vertical walls (two 12×8 and two 10×8) are counted and the floor and ceiling are correctly left out.
Find the area of the four walls
The four walls come in two matching pairs.
A wall is just a rectangle, and its area is width times height.
4.MD.A.3Draw A DiagramAdd up one bedroom's walls
One room's walls total 352.
Opposite walls come in matching pairs, so double each size and add the two pairs.
Opposite walls come in matching pairs, so each size is doubled and the two pairs are added.
▸ Why?
The same wall area repeated twice is a count of equal groups, which multiplying records.
▸ Why?
The room's surface is exactly its four walls put together, so their areas add to the total.
Subtract the doorways and windows
Subtracting the openings per room leaves 292.
Openings are holes in the wall, so their area is removed from what gets painted.
4.NBT.B.4Identify SubproblemsMultiply by the three bedrooms
Multiplying by the three rooms gives 876, choice (E).
Three identical rooms means three equal amounts, so multiply one room's area by three.
4.NBT.B.5Identify SubproblemsBreak a room into its four rectangular walls, add them up, take out the openings, then multiply by the number of identical rooms.
- Find the area of the four walls
- Add up one bedroom's walls
- Subtract the doorways and windows
- Multiply by the three bedrooms