Calculate the Area of a Rectangle: Visual Geometry Problem

Question

Look at the rectangle in the figure.

What is its area?

00:00 Express the area of the rectangle

00:03 The formula for calculating the area of a rectangle is side times side

00:10 When opening the parentheses, note that each term multiplies all terms

00:14 For example, notice how 4X multiplies each term and only then X squared

00:28 Now let's solve each multiplication separately

00:41 Let's arrange the equation

00:46 And this is the solution to the question

We know that the area of a rectangle is equal to its length multiplied by its width.

We begin by writing an equation with the available data.

$(4x+x^2)\times(3x+8+5x)$

Next we use the distributive property to solve the equation.

$(4x\times3x)+(4x\times8)+(4x\times5x)+(x^2\times3x)+(x^2\times8)+(x^2\times5x)=$

We then solve each of the exercises within the parentheses:

$12x^2+32x+20x^2+3x^3+16x^2+5x^3=$

Finally we add up all the coefficients of X squared and all the coefficients of X cubed and we obtain the following:

$48x^2+8x^3+32x$

$8x^3+28x^2+44x$