Given: A figure is given.
Required: to determine the expression for the area of the figure. Also, determine the area when x=2.
Explanation: The area of the figure can be determined by dividing the figure as shown below-
Now, DEFG and ABCG represent rectangles. The dimensions of the rectangle DEFG is (2x+4) by (7x+2), and of the rectangle, ABCG is (4x+2) by BC where BC is-
[tex]\begin{gathered} BC=(3x+5)-(2x+4) \\ =x+1 \end{gathered}[/tex]
Hence, the expression for the area is-
[tex]\begin{gathered} A=(2x+4)(7x+2)+(4x+2)(x+1) \\ A=(14x^2+4x+28x+8)+(4x^2+4x+2x+2) \end{gathered}[/tex]
Further solving-
[tex]\begin{gathered} A=14x^2+32x+8+4x^2+6x+2 \\ =18x^2+38x+10\text{ sq units} \end{gathered}[/tex]
Substituting x=2 as follows-
[tex]\begin{gathered} A=18(2^2)+38(2)+10 \\ =72+76+10 \\ =158\text{ sq units} \end{gathered}[/tex]
Final Answer: The expression for the area of the figure is-
[tex]A=18x^2+38x+10\text{ sq un}\imaginaryI\text{ts}[/tex]
The area when x=2 is 158 sq units.
