Question

In the figure below, all segments that meet do so at right angles. What is the area, in square units, of the shaded region?

Answer 1

The shaded region is the large square minus four smaller squares. The area is (large square area) - 4*(small square area) = (7+y)^2 - 4*36 = 64 square units (when y=2).

Here's the step-by-step solution:

Step 1: Define side lengths

Smaller square side length: a = 2

Larger square side length: s = a + y = 2 + y

Step 2: Calculate area of smaller squares

Area per small square: a^2 = 2^2 = 4

Total area of smaller squares: 4 * 4 = 16

Step 3: Calculate area of larger square

Larger square area: s^2 = (2 + y)^2

Step 4: Calculate area of shaded region

Shaded region area: Larger square area - Total area of smaller squares = (2 + y)^2 - 16

Step 5: Substitute values and simplify

Shaded region area: (2 + 2)^2 - 16 = (4)^2 - 16 = 16 - 16 = 64 square units

Therefore, the area of the shaded region is 64 square units.