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 15b 12a

Explanation:

Step1: Count the number of small right - triangles

Count the small right - triangles in the shaded region. There are 8 small right - triangles.

Step2: Calculate the area of the triangular part

Since the area of one small right - triangle is \(A\) \(cm^{2}\), the area of 8 small right - triangles is \(8A\) \(cm^{2}\).

Step3: Consider the square part

The area of the square in the shaded region is \(B\) \(cm^{2}\).

Step4: Find the total area of the shaded region

The area of the shaded region is the sum of the area of the 8 small right - triangles and the area of the square, which is \(8A + B\) \(cm^{2}\).

Answer:

B. \(8A + B\)