ISEE Upper Level Quantitative : How to find the area of an equilateral triangle

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

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Example Questions

Example Question #1 : How To Find The Area Of An Equilateral Triangle

 is an equilateral triangle. Points  are the midpoints of , respectively.  is constructed.

Which is the greater quantity? 

(a) The area of 

(b) Twice the area of 

Possible Answers:

(a) and (b) are equal.

(b) is greater.

It is impossible to tell from the information given.

(a) is greater.

Correct answer:

(a) is greater.

Explanation:

If segments are constructed in which the endpoints form the midpoints of the sides of a triangle, then four triangles, congruent to each other and similar to the larger triangle, are formed. Therefore, one of these triangles - specifically,  - would have one-fourth the area of . This means  has more than twice the area of .

Note that the fact that the triangle is equilateral is irrelevant.

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