Question

In the given figure, a square is cut as shown in the first figure and rearranged to form a big square as shown in the second figure. Then, the side of the small square(hole) and area of the big square in the second figure respectively is _____.

• A. 2cm, 29 sq.units
• B. 3cm, 34 sq.units
• C. 1cm, 26 sq.units
• D. 4cm, 41 sq.units

Answer 1

The correct option is A

2cm, 29 sq.units

In the first figure, The square is of the side = 1.5cm + 3.5cm = 5cm

Area of the first square = $5\times 5=25sq.units$

It is cut and rearranged to get a bigger square as shown in the second figure with a square hole in the middle

The side of the square hole in the middle = 3.5 - 1.5cm = 2cm

The area of the square hole in the middle = $2\times 2=4sq.units$

$\therefore$ The area of the bigger square = area of the 1st square + area of the square hole in the middle

$\therefore$ The area of the bigger square = 25 sq.units + 4 sq.units = 29 sq.units