Question

Rectangle ABCD has an area of 50 cm squared. Rectangle EFGH is similar to rectangle ABCD and larger with a scale factor of 4 between them. What is the area of rectangle EFGH in cm squared?

Answer 1

To find the area of rectangle EFGH, we can use the scale factor between rectangle ABCD and rectangle EFGH.

Since the two rectangles are similar and the scale factor between them is 4, we need to square the scale factor to find the ratio of their areas. The area of similar figures is proportional to the square of the scale factor.

The formula to calculate the area of rectangle EFGH is given by:
\[
\text{Area of EFGH} = \text{Area of ABCD} \times \text{(Scale Factor)}^2
\]

Given:
- Area of rectangle ABCD = 50 cm²
- Scale Factor = 4

Now calculate the area of rectangle EFGH:
\[
\text{Area of EFGH} = 50 \, \text{cm}^2 \times (4^2)
\]
\[
= 50 \, \text{cm}^2 \times 16
\]
\[
= 800 \, \text{cm}^2
\]

Therefore, the area of rectangle EFGH is \( \boxed{800} \) cm².