Question

The area of one of the small right triangles outlined in blue is A cm2, while the area of the square outlined in red is B cm2. Which expressions show the area of the shaded region in terms of A and B? Check all that apply.

4A + B
8A + B
2A + B
1.5B
12A

Answer 1

I don't have the diagram — can you either upload the picture or describe exactly which parts are shaded (e.g. "the four corner triangles are shaded" or "everything except the red square is shaded")?

If it helps, here are the steps you can use to decide which expressions are correct once I can see/know the picture:

1. Count how many of the small blue right triangles are included in the shaded region. If n of those triangles are shaded, their total area is n·A.
2. Decide whether the red square (area B) is included in the shaded region. If it is, add B; if not, do not add B.
3. The shaded area will be of the form nA (+ B if the red square is included). Compare that to each choice:
- 4A + B corresponds to n = 4 and red square included.
- 8A + B corresponds to n = 8 and red square included.
- 2A + B corresponds to n = 2 and red square included.
- 1.5B would mean the shaded area equals 3/2 of the red square (compare with nA + B).
- 12A corresponds to n = 12 and red square not included.

Send the diagram or a precise description and I’ll pick which choices are correct.