Question number 18. The large equilateral triangle shown in the picture here was divided into 36 smaller equilateral triangles, each of an area of one centimeter squared. Question is, what is the area of the triangle shaded in green here with vertices A, B, and C? Okay, so the way we compute that is to notice that the triangle here straddles three parallelograms, and let me shade those in red. So, for example, from vertex C along this line here like that, and then across we have a parallelogram, and exactly half of it belongs to the green triangle. Exactly half its area belongs to the green triangle. So let's compute. Here we have area equal to, well, inside of that parallelogram are exactly four equilateral triangles, so one half times four centimeters squared, so that is two centimeters squared, and we keep going like that. Then in the next parallelogram we can find, which is over here, we also notice that half of it belongs to the green triangle, and here the area would be exactly half of, and then how many equilateral triangles do we have in there? And we can count them, and we have six of them, times six centimeters squared, and that gives us three centimeters squared for the area of the green triangle belonging to this parallelogram. And finally, in orange, we have here our last parallelogram. Let me trace that out like so, and its area would be exactly equal to, again, half here times, and then there are twelve of these equilateral triangles, so times twelve centimeters squared, and that gives us six centimeters squared as the area of the green triangle belonging to that orange parallelogram, and then we just sum all of these up, so area of ABC, of triangle ABC, is equal to six centimeters squared plus two centimeters squared plus three centimeters squared, and so that comes out to eleven centimeters squared, and so we choose that answer, which is choice E.

shaded triangle

equilateral triangles

parallelograms

area calculation

geometry problem