Question

expressing the area of a composite figure 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

Explanation:

Answer:

4A + B, 1.5B, 12A

(Note: To determine this, we analyze the composite figure: The square (area B) is divided into 8 small right triangles (each with area A? Wait, no—wait, the small blue triangles: let's see, the square has 8 triangles? Wait, no, the square outlined in red: if the square's area is B, and it's divided into 8 triangles? Wait, no, maybe the square is divided into 8 triangles, but the small blue triangles (the ones outside the square?) Wait, the figure: the red square is divided into 8 triangles (since it's a square with diagonals and midlines, making 8 congruent right triangles). Then the shaded region: let's count the triangles. The square has 8 triangles (each with area A? Wait, no, the problem says "the area of one of the small right triangles outlined in blue is A cm²". Wait, maybe the square (B) is made of 8 triangles, so each triangle in the square has area B/8. But the blue triangles outside: let's see, the shaded region has 4 triangles outside the square? Wait, no, the figure: looking at the diagram, the red square is in the center, and there are 4 blue triangles attached to the square (like a pinwheel), and the square itself is divided into 8 triangles? Wait, no, maybe the square (B) is composed of 8 small triangles (each with area A), so B = 8A? Wait, no, the options: 4A + B, 8A + B, 2A + B, 1.5B, 12A. Let's check: If the square (B) is made of 8 triangles (each A), then B = 8A. Then the shaded region: how many triangles? The square has 8 triangles, and there are 4 more triangles outside? Wait, no, the diagram: the red square is divided into 8 triangles (so 8A = B? Wait, no, the problem says "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". So the square (B) is composed of 8 small triangles (each with area A)? Wait, no, maybe the square is divided into 8 triangles, so B = 8A. Then the shaded region: let's count the triangles. The square has 8 triangles (area B = 8A), and there are 4 more triangles outside (each A), so total area is 8A + 4A? No, that doesn't match. Wait, maybe the square is divided into 8 triangles, so each triangle in the square has area B/8. But the small blue triangles (the ones outside) have area A. Wait, the options: 4A + B, 1.5B, 12A. Let's check 1.5B: if B is 8A, then 1.5B = 12A. And 4A + B: if B is 8A, then 4A + 8A = 12A. So 4A + B = 12A (since B = 8A), and 1.5B = 12A (since 1.5*8A = 12A). So the correct expressions are 4A + B, 1.5B, and 12A. )