Answer:
[tex] A_{\textsf{parallelogram}} = 98 \, \textsf{cm}^2 [/tex]
[tex] A_{\textsf{rectangle}} = 147 \, \textsf{cm}^2 [/tex]
[tex] \textsf{Total Area} = 245 \, \textsf{cm}^2 [/tex]
Step-by-step explanation:
To find the area of the composite figure, we first need to find the area of each individual component and then sum them up.
Area of the Parallelogram:
Given:
- Base of the parallelogram [tex]= 7 \, \textsf{cm}[/tex]
- Height of the parallelogram [tex]= 14 \, \textsf{cm}[/tex]
The area [tex]A[/tex] of a parallelogram is given by the formula:
[tex] A_{\textsf{parallelogram}} = \textsf{Base} \times \textsf{Height} [/tex]
[tex] A_{\textsf{parallelogram}} = 7 \times 14 [/tex]
[tex] A_{\textsf{parallelogram}} = 98 \, \textsf{cm}^2 [/tex]
Area of the Rectangle:
Given:
- Length of the rectangle [tex]= 21 \, \textsf{cm}[/tex]
- Width of the rectangle [tex]= 7 \, \textsf{cm}[/tex]
The area [tex]A[/tex] of a rectangle is given by the formula:
[tex] A_{\textsf{rectangle}} = \textsf{Length} \times \textsf{Width} [/tex]
[tex] A_{\textsf{rectangle}} = 21 \times 7 [/tex]
[tex] A_{\textsf{rectangle}} = 147 \, \textsf{cm}^2 [/tex]
Now, to find the total area of the composite figure, we add the areas of the parallelogram and the rectangle:
[tex] \textsf{Total Area} = A_{\textsf{parallelogram}} + A_{\textsf{rectangle}} [/tex]
[tex] \textsf{Total Area} = 98 + 147 [/tex]
[tex] \textsf{Total Area} = 245 \, \textsf{cm}^2 [/tex]
So, the total area of the composite figure is [tex]245 \, \textsf{cm}^2[/tex].
