Area of the Square: Express using

Remember that the area of a square is equal to the side of the square raised to the 2nd power.

Formula for the square area:

$A=L^2$

We substitute our values into the formula:

$A=(x+y)^2$

Remember that the area of the square is equal to the side of the square raised to the 2nd power.

Formula for the area of the square:

$A=L^2$

Then we substitute our values into the formula:

$A=(4+x)^2$

Remember that the area of the square is equal to the side of the square raised to the 2nd power.

Formula for the area of the square:

$A=L^2$

We substitute our values into the formula:

$A=(a-b)^2$

The area of a square can be obtained by squaring the measurement of one of its sides.

The formula for the area of a square is:

$S=a^2$

Let's therefore insert the known data into the formula:

$S=x^2y^2$

The area of a square is equal to measurement of one of its sides squared.

Below is the formula for the area of a square :

$S=a^2$

Let's now insert the known data into the formula:

$S=\frac{20^2}{y^2}=\frac{400}{y^2}$

The area of a square is equal to the measurement of one of its sides squared.

The formula for the area of a square is:

$S=a^2$

Hence let's insert the given data into the formula as follows:

$S=(2+x)^2$

The area of a square is equal to the measurement of one of its sides squared.

The formula for the area of a square is:

$S=a^2$

Hence let's insert the given data into the formula as follows:

$S=(4x+4y)^2$

The area of a square is equal to the measurement of one of its sides squared.

The formula for the area of a square is:

$S=a^2$

Hence let's insert the given data into the formula as follows:

$S=(6+4x)^2$

The area of a square is equal to the measurement of one of its sides squared.

The formula for the area of a square is:

$S=a^2$

Hence let's insert the given data into the formula as follows:

$S=(9+y)^2$

The area of a square is equal to the measurement of one of its sides squared.

The formula for the area of a square is:

$S=a^2$

Hence let's insert the given data into the formula as follows:

$S=\frac{10^2}{x^2}=\frac{100}{x^2}$

The area of a square is equal to the measurement of one of its sides squared.

The formula for the area of a square is:

$S=a^2$

Hence let's insert the given data into the formula as follows:

$S=(x+7y)^2$

The area of a square is equal to the side of the square raised to the 2nd power:

$S=a^2$

$S=(8-3x)^2$

$S=(-3x+8)^2$

The area of a square is equal to the value of one of its sides squared.

Below is the formula for the area of a square:

$S=a^2$

Let's therefore insert the known data into the formula as follows:

$S=\frac{x^2}{y^2}$

Remember that the area of a square is equal to the side of the square squared.

The formula for the area of a square is:

$S=a^2$

Finally, substitute the data into the formula:

$S=(5+2x)^2$

Remember that the area of the square is equal to the side of the square raised to the 2nd power.

The formula for the area of the square is

$A=L^2$

We place the data in the formula:

$A=(x-7)^2$

First, recall the formula for calculating square area:

The area of a square (where all sides are equal and all angles are $90\degree$) with a side length of $a$(length units - u)

, is given by the formula:

$\boxed{ S_{\textcolor{red}{\boxed{}}}=a^2}$(square units - sq.u),

Let's proceed to solve the problem:

First, let's mark the square's vertices with letters: $ABCD$

Next, considering the given data (that the square's side length is: $x+1$ cm), apply the above square area formula in order to express the area of the given square using its side length-$AB=BC=CD=DA= x +1$ (cm):

$S_{\textcolor{red}{\boxed{}}}=AB^2\\ \downarrow\\ S_{\textcolor{red}{\boxed{}}}=(x+1)^2$(sq.cm)

Continue to simplify the algebraic expression that we obtained for the square's area. This can be achieved by using the shortened multiplication formula for squaring a binomial:

$(c+d)^2=c^2+2cd+d^2$ Therefore, we'll apply this formula to our square area expression:

$S_{\textcolor{red}{\boxed{}}}=(x+1)^2 \\ \downarrow\\ \boxed{S_{\textcolor{red}{\boxed{}}}=x^2+2x+1}$(sq.cm)

The correct answer is answer D.

To find the area of a square with side length $x + 1$, we apply the formula for the area of a square, which is side squared. This means we need to calculate $(x + 1)^2$.

Here are the steps to solve the problem:

• Step 1: Identify the expression for the side length. The side length of the square is given as $x + 1$.
• Step 2: Use the formula for the area of a square: $(\text{side})^2$.
• Step 3: Substitute the side length with $x + 1$: $(x + 1)^2$.
• Step 4: Expand the expression using the formula for the square of a sum: $(a + b)^2 = a^2 + 2ab + b^2$, where $a = x$ and $b = 1$.
• Step 5: Calculation:
• $(x + 1)^2 = x^2 + 2(x)(1) + 1^2$
• $(x + 1)^2 = x^2 + 2x + 1$

Therefore, the algebraic expression for the area of the square is $x^2 + 2x + 1$.