AMC 10 · 2023 · #4
Grade 5 geometry-2dPick an answer.
The whole problem is a units trap. Tool #8 (Analyze Units) forces both length and width into centimeters before multiplying — the only safe path to cm². The choice list is spread across factors of 10 on purpose (162.5, 1,625, 16,250, 162,500, 1,625,000), so an off-by-a-factor-of-10 conversion mistake lands on a wrong choice. A quick diagram (Tool #1) of a very long thin rectangle reminds the student which dimension is which and that the formula is just length × width.
Width in centimetres
Convert the width to centimetres.
Going from a smaller unit (mm) to a larger one (cm), the number gets smaller — Grade 5 unit conversion.
Going from a smaller unit to a larger one makes the number smaller, and the reverse makes it larger.
▸ Why?
A larger unit is a fixed bundle of smaller ones, so it takes fewer of them to say the same length.
▸ Why?
Because the bundles here are powers of ten, converting only slides the decimal point.
Length in centimetres
Convert the length to the same unit.
Going from a larger unit (m) to a smaller one (cm), the number gets bigger.
5.MD.A.1Analyze The UnitsWrite the area
The area is width times length.
Length times width for a rectangle — Grade 4 area formula.
4.MD.A.3Draw A DiagramCompute it
Multiplying gives 1625.
Splitting 0.65 into 65/100 turns the decimal multiplication into clean whole-number arithmetic — Grade 5.
5.NBT.B.7Analyze The UnitsThis AMC 12 problem only needs Grade 5 unit conversion — get both sides into centimeters first, then multiply 2500 × 0.65 to land on 1,625 cm².