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Two shapes are drawn on the same squared paper. Shape P covers 21 full squares and 10 squares that are each exactly half covered. Shape Q covers 25 full squares and 4 exactly-half squares. Which shape has the greater area?

Class 6MensurationMensuration
  • AShape P
  • BShape Q
  • CBoth cover exactly the same area.
  • DShape P, because its outline touches more squares.

Step-by-Step Solution

Two exactly-half squares together make one whole square. Shape P = 21 + (10 ÷ 2) = 26 square units; Shape Q = 25 + (4 ÷ 2) = 27 square units. So Q is larger, by 1 square unit. Touching more squares is not the same as covering more area.
Answer: B) Shape Q

Key idea: Area — the surface inside

Area measures how much flat space a shape covers. The unit is a **square** of side 1 — so (square centimetres), (square metres), etc. To measure the area of a rectangle visually, imagine covering it with 1-cm squares: count them. A rectangle 5 cm by 3 cm holds little squares, so its area is . The general formula is the same idea: area of rectangle = .

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