Question

Four square pieces are cut from the corners of a square sheet of metal. As the size of the small squares increases the remaining area decreases, as shown. If this pattern continues, what will be the difference the first square's shaded area and the fifth square's shaded area?

• A. $4$ square units
• B. $24$ square units
• C. $49$ square units
• D. $96$ square units

Answer 1

The correct option is D $96$ square units

Area of $I^{st}$ square $=$ $a^2-4\times 1^2=a^2-4$

Area of $V^m$ square $=$ $a^2-4\times 5^2=a^2-100$

Difference $=$ $a^2-4-a^2+100=96$ square units