A rectangle has the dimensions of $8 f t \times 4 f t .$ Calculate the area of the rectangle produced when it is scaled by a scale factor of 4.

128 f t^{2}

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512 f t^{2}

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256 f t^{2}

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1024 f t^{2}

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Solution

The correct option is B $512 f t^{2}$
Dimensions of the given rectangle $= 8 f t \times 4 f t$

Scale factor $= 4$

There are two ways to calculate the area of the larger rectangle.

Method 1:
Calculate the dimensions of the scaled rectangle.

Dimensions of the scaled rectangle will be:

Length $= 8 f t \times 4 = 32 f t$

Breadth $= 4 f t \times 4 = 16 f t$

Area $=$ Length $\times$ Breadth

Area $= 32 \times 16 f t^{2} = 512 f t^{2}$

Method 2:
Multiply the area of the given rectangle by the square of the scale factor.

Area of the given rectangle $= 8 \times 4 = 32 f t^{2}$

Area of the scaled rectangle $= 32 \times (4)^{2} f t^{2}$

$= 32 \times 16 f t^{2} = 512 f t^{2}$

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A rectangle has the dimensions of 8 ft×4 ft. Calculate the area of the rectangle produced when it is scaled by a scale factor of 4.

A rectangle has the dimensions of $8 f t \times 4 f t .$ Calculate the area of the rectangle produced when it is scaled by a scale factor of 4.