The area of an equilateral triangle of side "s" is s^2*sqrt(3)/4. So the volume of the slices in your problem is
(x - x^2)^2 * sqrt(3)/4.
Integrating from x = 0 to x = 1, we have
[(1/3)x^3 - (1/2)x^4 + (1/5)x^5]*sqrt(3)/4
= (1/30)*sqrt(3)/4 = sqrt(3)/120 = about 0.0144.
Since this seems quite small, it makes sense to ask what the base area might be...integral from 0 to 1 of (x - x^2) dx = (1/2) - (1/3) = 1/6. Yes, OK, the max height of the triangles occurs where x - x^2 = 1/4, and most of the triangles are quite a bit shorter...
D, because it said that Krissy had equally distributed the bagels to each child, so 32/8=4, and then it asked how many bagels did the girls get all together, so it's 4x3=12
There are 16 smaller triangles within the main large one. .25=1/4, so your fraction is 1/4. 1/4 of 16 is 4, because 4+4+4+4=16. So colour in 4 triangles. Hope this helps!
