To solve the problem, follow these steps:
1. Understand the ratio: The ratio of the areas of the two squares is given as [tex]\( \frac{4}{5} \)[/tex]. This means that for every 5 units of area in the bigger square, the smaller square has 4 units of area.
2. Identify the area of the bigger square: It is given that the area of the bigger square is [tex]\( 475 \, \text{cm}^2 \)[/tex].
3. Calculate the area of the smaller square:
- Using the given ratio [tex]\( \frac{4}{5} \)[/tex], we can find the area of the smaller square.
- Multiply the area of the bigger square by the ratio of the smaller square:
[tex]\[
\text{Area of the smaller square} = \text{Area of the bigger square} \times \frac{4}{5}
\][/tex]
- Substituting the known value:
[tex]\[
\text{Area of the smaller square} = 475 \, \text{cm}^2 \times \frac{4}{5}
\][/tex]
- This calculation results in:
[tex]\[
\text{Area of the smaller square} = 380 \, \text{cm}^2
\][/tex]
4. Calculate the total area of both squares:
- Add the area of the smaller square to the area of the bigger square:
[tex]\[
\text{Total area} = \text{Area of the bigger square} + \text{Area of the smaller square}
\][/tex]
- Substituting the values:
[tex]\[
\text{Total area} = 475 \, \text{cm}^2 + 380 \, \text{cm}^2
\][/tex]
- This calculation results in:
[tex]\[
\text{Total area} = 855 \, \text{cm}^2
\][/tex]
Therefore, the area of the smaller square is [tex]\( 380 \, \text{cm}^2 \)[/tex] and the total area of both squares is [tex]\( 855 \, \text{cm}^2 \)[/tex].
