The dimensions of a rectangle are 8cm×4cm. If it is scaled by a factor of 4, what will the area of the scaled rectangle be?
A
128 sq cm
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B
512 sq cm
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C
1024 sq cm
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D
256 sq cm
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Solution
The correct option is B512 sq cm Dimensions of the rectangle =8cm×4cm
Scale factor =4
There are various methods to calculate the area of the new rectangle.
Method 1: Calculate the dimensions of the scaled rectangle.
Dimensions of the scaled rectangle will be:
New length =8cm×4=32cm
New width =4cm×4=16cm
New area = length× breadth ⇒ Area of the scaled rectangle =32×16=512sqcm
Method 2: Multiply the area of the given rectangle by the square of the scale factor.
Let’s say the scaling factor is k
New length =8×k=8kcm
New width =4×k=4kcm
Area of the scaled rectangle =(8k)×(4k)sqcm =32×k2sqcm
Here, 32 is the area of the original rectangle. Multiply it by the square of the scale factor to find the area of the scaled rectangle.
In this case k=4. Therefore,
Area of the given rectangle =8×4=32sqcm
Area of the scaled rectangle =32×(4)2=32×16 ⇒ Area of the scaled triangle =512sqcm