SAT Math formula sheet · all 24 · Geometry and Trigonometry · #21 of 24

How area and volume scale on the SAT: How It Is Tested

Area and volume

Proportionality diagram for the SAT: If the sides are k times bigger, the area is k squared times bigger and the volume is k cubed times bigger. Area is unit
What it is really testingIf the sides are k times bigger, the area is k squared times bigger and the volume is k cubed times bigger. Area is units squared, volume is units cubed. One calculation, not a whole recomputation.

The question from the sheet

Hard
SAT Geometry and Trigonometryanswer 17956
The length of each side of square AA is 134134 times the length of each side of square BB. The area of square AA is kk times the area of square BB. What is the value of kk?
Student-produced response: 17956

How the diagram applies

  1. Sides scale by kk, area scales by k2k^{2}.
  2. Sides are 134134 times bigger, so the area is 1342=17,956134^{2} = 17{,}956 times bigger.

Answer: 17956

That is 1 of 24.

The whole sheet is one page per formula, each one solved on a real SAT question. Print it, stick it on the wall, scan any diagram to get back here.

Download the sheet (PDF)Watch this one solved →

The PDF needs no account. The video, the clean diagrams and practice on this skill need a free one, and never a card.

All 24 diagrams

Common Questions

It comes up as an SAT area and volume question. If the sides are k times bigger, the area is k squared times bigger and the volume is k cubed times bigger. Area is units squared, volume is units cubed. One calculation, not a whole recomputation.

Sides scale by k, area scales by k^2. Sides are 134 times bigger, so the area is 134^2 = 17,956 times bigger.

No. The SAT reference sheet is twelve geometry formulas and three notes, and Proportionality is not one of them. It is one of the 24 things the test expects you to know without being given them. See what the reference sheet does cover at /blog/sat-math-reference-sheet.