To determine the total area of the five rooms, we need to calculate the area of the rooms separately and then add those areas together.
1. There are three rooms, each with a side length of 13 feet. The area of one such square room is given by:
[tex]\[
\text{Area of one room} = \text{side}^2 = 13^2
\][/tex]
Therefore, the total area for three rooms is:
[tex]\[
\text{Total area for three rooms} = 3 \times 13^2
\][/tex]
2. There are two rooms, each with a side length of 15 feet. The area of one such square room is given by:
[tex]\[
\text{Area of one room} = \text{side}^2 = 15^2
\][/tex]
Therefore, the total area for two rooms is:
[tex]\[
\text{Total area for two rooms} = 2 \times 15^2
\][/tex]
3. To find the total area of the five rooms, we sum the areas of the three rooms and the two rooms:
[tex]\[
\text{Total area} = (3 \times 13^2) + (2 \times 15^2)
\][/tex]
The correct expression that shows the total area is:
[tex]\[
\left(3 \times 13^{\wedge} 2 \right) + \left( 2 \times 15^{\wedge} 2 \right)
\][/tex]
Therefore, the correct answer is:
A. [tex]\(\left(3 \times 13^{\wedge} 2\right)+\left(2 \times 15^{\wedge} 2\right)\)[/tex]
