Twelve 1 by 1 squares form a rectangle, as shown. What is the total area of the shaded regions?
(A) 8
(B) 9
(C) 10
(D) 11
(E) 12

![](https://cdn.mathpix.com/cropped/2024_04_20_6ed09463f225f8ba1f07g-081.jpg?height=268&width=220&top_left_y=991&top_left_x=1343)
Solution 1

The total area of the rectangle is $3 \times 4=12$.

The total area of the shaded regions equals the total area of the rectangle (12) minus the area of the unshaded region.

The unshaded region is a triangle with base of length 1 and height 4; the area of this region is $\frac{1}{2}(1)(4)=2$.

Therefore, the total area of the shaded regions is $12-2=10$.

## Solution 2

The shaded triangle on the left has base of length 2 and height of length 4 , so has an area of $\frac{1}{2}(2)(4)=4$.

The shaded triangle on the right has base of length 3 (at the top) and height of length 4 , so has an area of $\frac{1}{2}(3)(4)=6$.

Therefore, the total area of the shaded regions is $4+6=10$.

ANSWER: (C)