Find an expression for the area of the figure!?

Question

I should totally remember this because my younger brother just finished up Algebra 2 but I don't. The problems that I have are to find an expression for the area of a rectangle and the are of the square.

The rectangle has a HEIGHT of x+y

The rectangle has a LENGTH of 2y

I just need an equation that I could set up with any number to solve it.

The square obviously has the same number of sides of the same length and that is x+3y

If you really want to help the numbers im substituting in the equation that you will hopefully give are, for the RECTANGLE are x=2 and y=3

The SQUARE x=5 y=2

Please Help!! Thanks!

Answer 1

Area of rectangle

= height*length

= (x+y)*(2y)

= 2xy+2y^2

Area of square

=[(x+3y)^2]*6 surfaces

= 6x^2+36xy+54y^2

Answer 2

The formula used to calculate the area of a rectangle is Length (L) x Width (W).( I think that your height is referring to width, but it amounts to the same answer either way.) The answer is expressed in square units (ex. sq in or sq ft).  The formula to calculate the area of a square is basically the same as above, because a square is just a "special" rectangle in that all 4 sides are of equal length.

Rectangle : A = L x W   (Formula)

A = 2y (x + y)   (Expression)

Simplified expression:

Distribute the 2y. Multiply 2y times x, then 2y times y

= 2xy + 2y^2  (y^2 means "y squared")

Plug in your numbers: 2(2)(3) + 2(3)^2 = 12+(2)9 = 12+18=30    

CHECK: W = x + y = 2 + 3 = 5

                 L = 2y = 2(3) = 6

                 A = L x W = 6 x 5 = 30

Square: Area = s^2   (Formula) (where s = "side", s^2 = "side squared")

A = (x + 3y)^2    (Expression)

(x + 3y)(x + 3y) = x^2 + 6xy + 9y^2

Substituting x=5 and y=2 into x^2 + 6xy + 9y^2

(5)^2 + 6(5)(2) + 9(2)^2

= 25 + 60 + 36 = 121

CHECK:

A = (x + 3y)^2

[(5) + 3(2)]^2 =

[5 + 6]^2 = (11)^2 = 121