Question

Write an expression for the area of the figure in terms of ( x ) and ( y ). Simplify your expression.

Answer 1

The expression for the area of the figure in terms of
`\(x\) and \(y\) is \(A = x^2 + 2xy\).`

Step-by-step explanation:

The given figure appears to be a rectangle with a square attached to one side. To express the area in terms of
`\(x\) and \(y\)`, we break down the figure into its component shapes: a square with side length
`\(x\)` and a rectangle with dimensions
`\(x\) (length) and \(y\)` (width).

The area of the square is
`\(x^2\), and the area of the rectangle is \(xy\).`Since there are two identical rectangles in the figure, we multiply the area of one rectangle by 2, resulting in
`\(2xy\).` Adding the areas of the square and the rectangles gives the expression for the total area:
`\(A = x^2 + 2xy\).`

This expression can be further simplified by factoring out the common factor of
`\(x\) from the terms, yielding \(A = x(x + 2y)\).` This simplified form highlights the dependence of the area on the variables
`\(x\) and \(y\).`Therefore, the final expression
`\(A = x^2 + 2xy\)` represents the area of the given figure in terms of
`\(x\) and \(y\).`