ISEE Upper Level Quantitative : How to find the area of a hexagon

Study concepts, example questions & explanations for ISEE Upper Level Quantitative

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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:

(b) is greater

It is impossible to tell from the information given

(a) and (b) are equal

(a) is greater

Correct answer:

(a) is greater


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.

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