Squares A, B, C and D are placed as shown in the diagram above. Two sm

Solution:

We are given the side lengths of squares B and C are both 1. Therefore, the side length of square A is 2. However, we are not given and we can’t determine the side length of square D. So let’s let the side length of square D be x. In addition, we will have a rectangle that encloses the 4 squares (see diagram below).



We see that if we subtract the sum of the areas of the two triangles above the shaded triangle and the trapezoid below it from the area of the rectangle that encloses the squares, then we have the area of the shaded triangle.

Area of the rectangle = 3(x + 2)

Area of the triangle above the shaded triangle to the right = ½(1)(1) = 1/2

Area of the triangle above the shaded triangle to the left = ½(3 - x)(x + 1) = ½(3 + 2x - x^2)

Area of the trapezoid below the shaded triangle = ½(x + 2)(x + 2) = ½(x^2 + 4x + 4)

Therefore, the area of the shaded triangle is:

Area = 3(x + 2) - [1/2 + ½(3 + 2x - x^2) + ½(x^2 + 4x + 4)]

Area = 3x + 6 - [1/2 + 3/2 + x - ½x^2 + ½x^2 + 2x + 2]

Area = 3x + 6 - [4 + 3x]

Area = 3x + 6 - 4 - 3x = 2

Answer: A