### All ISEE Upper Level Quantitative Resources

## Example Questions

### Example Question #1 : Hexagons

Which is the greater quantity?

(a) The area of a regular hexagon with sidelength 1

(b) The area of an equilateral triangle with sidelength 2

**Possible Answers:**

(a) and (b) are equal

It is impossible to tell from the information given

(a) is greater

(b) is greater

**Correct answer:**

(a) is greater

Explanation:

A regular hexagon with sidelength can be seen as a composite of six equilateral triangles, each with sidelength . Since area is in direct proportion to the square of the sidelength, the area of the equilateral triangle with sidelength is equal to that of four of those triangles. This makes the hexagon greater in area, and it makes (a) the greater quantity.

Robert

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Drew University, Bachelors, Math. University of Virginia-Main Campus, Masters, Applied Math.

Saige

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Stanford University, Bachelors, Mechanical Engineering. Stanford University, Current Grad Student, Mechanical Engineering.