Question

Write an expression to represent the area for figure in #4.Simplify the expression.Find the area when x=2.

Answer 1

Given: A figure is given.

Required: to determine the expression for the area of the figure. Also, determine the area when x=2.

Step-by-step 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-

`\begin{gathered} BC=(3x+5)-(2x+4) \\ =x+1 \end{gathered}`

Hence, the expression for the area is-

`\begin{gathered} A=(2x+4)(7x+2)+(4x+2)(x+1) \\ A=(14x^2+4x+28x+8)+(4x^2+4x+2x+2) \end{gathered}`

Further solving-

`\begin{gathered} A=14x^2+32x+8+4x^2+6x+2 \\ =18x^2+38x+10\text{ sq units} \end{gathered}`

Substituting x=2 as follows-

`\begin{gathered} A=18(2^2)+38(2)+10 \\ =72+76+10 \\ =158\text{ sq units} \end{gathered}`

Final Answer: The expression for the area of the figure is-

`A=18x^2+38x+10\text{ sq un}\imaginaryI\text{ts}`

The area when x=2 is 158 sq units.