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A square plot and a rectangular plot each have an area of . The rectangle is 18 m long. Which plot needs LESS fencing?

Class 7Perimeter and AreaPerimeter and Area
  • AThe square, needing 48 m against 52 m
  • BThe rectangle, needing 52 m against 48 m
  • CBoth need 48 m of fencing
  • DCannot be decided without the rectangle's width

Step-by-Step Solution

Square: sid → side = 12 m, perimeter = m. Rectangle: breadth = 144 ÷ 18 = 8 m, perimeter = m. Equal AREAS do not mean equal perimeters — the square saves 4 m of fencing. The rectangle's width is not missing; it follows from the area.
Answer: A) The square, needing 48 m against 52 m

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

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

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