Question

The dimensions of a rectangle are
$8cm\times 4cm.$ If it is scaled by a factor of $4,$ what will the area of the scaled rectangle be?

• A. $128$ sq cm
• B. $512$ sq cm
• C. $1024$ sq cm
• D. $256$ sq cm

Answer 1

The correct option is B $512$ sq cm

Dimensions of the rectangle
$=8cm\times 4cm$
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 $=8cm\times 4=32cm$
New width $=4cm\times 4=16cm$
New area $=\text{length}\times \text{breadth}$
$\Rightarrow$ Area of the scaled rectangle
$=32\times 16=512sqcm$

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 $=8\times k=8kcm$
New width $=4\times k=4kcm$
Area of the scaled rectangle $=\left(8k\right)\times \left(4k\right)sqcm$
$=32\times k^{2}sqcm$

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 $=8\times 4=32sqcm$
Area of the scaled rectangle $=32\times (4{)}^2=32\times 16$
$\Rightarrow$ Area of the scaled triangle
$=512sqcm$