Geo Brain Teaser

[snakeeyes1000]

I was just wondering how many of you could solve a geometry brain teaser.

A large equalateral triangle is formed by a trapezoid and a an equalateral triangle. The Smaller base of the trapezoid has the measure of 6 inches. How many square inches is in the total figure?

Express your answer in simplest radical form. Easy question really, first correct answer(with explanation) wins.

[bugzpodder]

I am sure that you are missing something from the question. giving me 6 inches isn't enough. i need another piece of information that deals with the larger equilateral triangle. ok imaginer a equilateral triangle with a side of 6 inches. extend the two of the sides towards one direction for n inches. then if you connect the new points, you'll form the larger equilateral triangle. from the side of the original equilateral triangle that hasn't been extended to the newly created side, thats a trapizoid. so the trapizoid could be anysize, so could the new equilateral triangle.

without the info, the area of the large equil. triangle would be:
(6+n)*(sqrt(3)/4)

[snakeeyes1000]

not true. look at it differently.

[bugzpodder]

lol ok, could you tell me where I went wrong, as if you follow my explaination, do you also get a trapizoid and a equalateral triangle? (of course, no need to give away the question).

[snakeeyes1000]

if you thought about the components of the large triangle and the trapezoid, using the six inches you can derive the rest. That's all I am saying now, because it is really very simple, if you know area and basic geometric principles.

[Alphanos]

The area is 0.5 * (h + (27^0.5)) * (6 + (2h / (3^0.5))), where h is the height of the trapezoid. There is no absolute answer without being able to determine the height; you can extend the trapezoid for any amount of distance to get a larger triangle.

An alternative format would be 3*27^0.5 (small triangle's area) + h * (6 + h/3^0.5) (trapezoid's area)

[DavidHooper]

Yup, agree with bugz and Alphanos.

[snakeeyes1000]

sorry, my mistake. The trapezoid and small triangle are of equal height.(1/2 or 50% the larger triangle)

[bugzpodder]

lol thats easy! the large triangle must be 4 times the size (ratio of 1:2 in terms of sides. so the area ratio is 1:4) the small triangle.

the size of smaller triangle is 6*sqrt(3)/4. so the larger triangle would be 6*sqrt(3)