Question

What is the area of the black portion in the square of side 16 cm?

Hint:

In visual puzzles, look for symmetry. If the figure is symmetric and covers half the square, no need to compute each small triangle separately.

Answer 1

Step 1: Total area of the square.
Side = 16 cm. \[ A_{\text{total}} = 16^2 = 256 \, \text{cm}^2 \] Step 2: Understand black region.
- The black shapes are arranged symmetrically inside the square.
- Each black shape is a star-like pattern that together forms exactly half the area of the square.
- This is a symmetry trick often used in reasoning questions.
Step 3: Compute black area.
Since the black region = $\tfrac{1}{2}$ of total area: \[ A_{\text{black}} = \frac{256}{2} = 128 \, \text{cm}^2 \] Final Answer: \[ \boxed{128 \, \text{cm}^2} \]