Tile-tiled Areas: Inductive Derivation

Froggy Jumps

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Explore area via tile counts.

John Angeles

Philippines

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Tile-tiled Areas: Inductive Derivation


Froggy Jumps Tile-tiled Areas: Inductive DerivationVersion en ligne Explore area via tile counts. par John Angeles 1 What is the formula for the area of a rectangle in terms of its length and width, using tile units? a Area = 2 × (length × width) b Area = length × width c Area = length + width 2 How can you inductively verify the area of a square using unit square tiles? a Tiles form a ring around the square b The number of tiles equals side length squared c Tiles count diagonally to get area 3 If a square has side length 5 units, how many unit tiles cover it? a 20 tiles b 25 tiles c 30 tiles 4 A rectangle 3 by 4 is tiled with unit squares. How many tiles are needed? a 7 tiles b 16 tiles c 12 tiles 5 What is the standard area unit when counting tiles on a plane? a Cubic units b Square units c Linear units 6 For a 1x1 square, what is the area in tiles? a 1 tile b 0 tiles c 2 tiles 7 If you double the side length of a square, how does the area change? a Area triples b Area multiplies by 4 c Area doubles 8 A rectangle is 2 by 7. What is its area in square units? a 21 square units b 9 square units c 14 square units 9 How many unit tiles cover a 2x2 square? a 4 tiles b 2 tiles c 8 tiles 10 Why does area scale with length when tiling with unit squares? a Because width is constant b Because perimeter increases c Because area counts how many unit tiles fit