The side of a square is increased to three times its original length. What happens to its area?

Class 7Perimeter and AreaPerimeter and Area

AIt becomes 3 times
BIt becomes 9 times
CIt becomes 6 times
DIt stays the same

Step-by-Step Solution

Area = sid

e^{2}

. If the side becomes 3

s

, the area becomes

(3 s)^{2} = 9 s^{2}

, so it is 9 times as large. The PERIMETER, being a length, does become just 3 times — mixing the two is the trap.

Answer: B) It becomes 9 times

Key idea: Parallelogram area

**Area of a parallelogram = base × height.**

Same idea as a rectangle, but the height is the perpendicular distance between the two parallel sides — NOT the slant length of the side. Pick any side as the base, drop a perpendicular to the opposite parallel side, measure that — that's the height.

Example: parallelogram with base 8 cm and perpendicular height 5 cm. Area =

8 \times 5 = 40 cm^{2}

. The slant side could be longer; doesn't matter for area.

Perimeter of a parallelogram = 2 × (one side + adjacent side).

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