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 cm2
The six-sided figure is what is left of the card, so its area is the rectangle minus the four cut-off triangles. The figure marks one triangle’s arms as 4 cm and 3 cm, and all four triangles are identical.
Area of the card \(=13\times6=78\) cm2
Area of one triangle \(\displaystyle =\frac{1}{2}\times4\times3=6\) cm2, so the four triangles cover 24 cm2
Area of the six-sided figure \(=78-24=54\) cm2