A boy was playing with a rectangular cardboard of dimensions 13 cm × 6 cm. While playing, he sliced off identical triangles from the corners of the cardboard in such a manner that a figure having all its sides equal was generated (as shown in the adjoining figure). The area of this six-sided figure is:

$54\, cm^2$

The correct answer is Option (2) → $54\, cm^2$

Step 1: Understand the figure

• Original rectangle: 13 cm × 6 cm
• From each corner, identical right triangles are cut, leaving a regular hexagon inside.
• Dimensions of the triangles given in the figure: base = 4 cm, height = 3 cm

So, each corner triangle area:

$\text{Area} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \times 3 = 6 \text{ cm}^2$

There are 4 triangles cut from corners → total area removed:

$4 \times 6 = 24 \text{ cm}^2$

Step 2: Area of the original rectangle

$\text{Area} = 13 \times 6 = 78 \text{ cm}^2$

Step 3: Area of the hexagon

$\text{Hexagon area} = \text{Rectangle area} - \text{Area of 4 triangles}$

$= 78 - 24 = 54 \text{ cm}^2$