Question

The area of a rectangle with dimensions $8cm\times 4cm$ is $32c{m}^2$. If the value of the scale factor is $4$, calculate the area of the larger rectangle formed by multiplying the scale factor.

• A. $128c{m}^2$
• B. $1024c{m}^2$
• C. $512c{m}^2$
• D. $256c{m}^2$

Answer 1

The correct option is C $512c{m}^2$

Given:

Area of the small rectangle $=32c{m}^2$

Dimensions of the small rectangle $=8cm\times 4cm$

Scale factor $=4$

Now, there are various methods to calculate the area of the larger rectangle.

Method - $1$: Calculate the dimensions of the larger rectangle

Dimensions of the larger rectangle will be:

Length $=8cm\times 4=32cm$

Breadth $=4cm\times 4=16cm$

Area $=$ Length $\times$ Breadth

Area $=32\times 16c{m}^2=512c{m}^2$

Method - $2$: Multiply the area of the small rectangle by the square of the scale factor

Area of the small rectangle $=32c{m}^2$

Area of the large rectangle $=32\times (4{)}^{2}c{m}^2$

$=32\times 16c{m}^2=512c{m}^2$