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

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

varsity tutors app store varsity tutors android store

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) is greater

It is impossible to tell from the information given

(b) is greater

(a) and (b) are equal

Correct answer:

(a) is greater

Explanation:

A regular hexagon with sidelength \(\displaystyle s = 1\) can be seen as a composite of six equilateral triangles, each with sidelength \(\displaystyle s = 1\). Since area is in direct proportion to the square of the sidelength, the area of the equilateral triangle with sidelength \(\displaystyle s = 2\) is equal to that of four of those triangles. This makes the hexagon greater in area, and it makes (a) the greater quantity.

Learning Tools by Varsity Tutors