Answer:
[tex] \textsf{Area}_{\textsf{square}} = 16 \, \textsf{in}^2 [/tex]
[tex] \textsf{Area}_{\textsf{rectangle}} = 14 \, \textsf{in}^2 [/tex]
[tex] \textsf{Area}_{\textsf{total}} = 30 \, \textsf{in}^2 [/tex]
Step-by-step explanation:
To find the total area of the figure, which includes a square and a rectangle, we add the individual areas of each shape.
Area of Square ([tex]\textsf{Area}_{\textsf{square}}[/tex]):
The area of a square is given by the formula [tex]A_{\textsf{square}} = \textsf{side} \times \textsf{side}[/tex].
Given: Side of the square = 4 in.
[tex] \textsf{Area}_{\textsf{square}} = 4 \times 4 [/tex]
[tex] \textsf{Area}_{\textsf{square}} = 16 \, \textsf{in}^2 [/tex]
Area of Rectangle ([tex]\textsf{Area}_{\textsf{rectangle}}[/tex]):
The area of a rectangle is given by the formula [tex]\textsf{Area}_{\textsf{rectangle}} = \textsf{length} \times \textsf{width}[/tex].
Given: Length of the rectangle = 7 in, Width of the rectangle = 2 in.
[tex] \textsf{Area}_{\textsf{rectangle}} = 7 \times 2 [/tex]
[tex] \textsf{Area}_{\textsf{rectangle}} = 14 \, \textsf{in}^2 [/tex]
Total Area of the Figure ([tex]\textsf{Area}_{\textsf{total}})[/tex]:
To find the total area, add the individual areas of the square and the rectangle.
[tex] \textsf{Area}_{\textsf{total}} = \textsf{Area}_{\textsf{square}} + A_{\textsf{rectangle}} [/tex]
[tex] \textsf{Area}_{\textsf{total}} = 16 + 14 [/tex]
[tex] \textsf{Area}_{\textsf{total}} = 30 \, \textsf{in}^2 [/tex]
Therefore, the total area of the figure is [tex]30 \, \textsf{in}^2[/tex].
