11. The ratio of the areas of two squares is [tex]$4: 5$[/tex]. If the area of the larger square is [tex]$475 \, cm^2$[/tex], what is the total area of both squares?



Answer :

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].