The length of each side of a square land shown in the figure is (a + b) units. In the corner of this land there is a square portion of length ‘b’ units is useless. Find the area of the portion of the land which is useful.

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Solution

Total area of the square land = (a + b)² = a² + 2ab + b²

Area of useless land = b²

∴ Useful land = a² + 2ab + b² − b² = (a² + 2ab) sq units

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The length of each side of a square land shown in the figure is (a + b) units. In the corner of this land there is a square portion of length ‘b’ units is useless. Find the area of the portion of the land which is useful.

Total area of the square land = (a + b)2 = a2 + 2ab + b2 Area of useless land = b2 ∴ Useful land = a2 + 2ab + b2 − b2 = (a2 + 2ab) sq units

Total area of the square land = (a + b)² = a² + 2ab + b²

Area of useless land = b²

∴ Useful land = a² + 2ab + b² − b² = (a² + 2ab) sq units