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:
Answer & explanation
Correct answer: option 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
$\text{Hexagon area} = \text{Rectangle area} - \text{Area of 4 triangles}$
$= 78 - 24 = 54 \text{ cm}^2$