Calculate Rectangle Area: Using Distributive Property with (9+4)(3+2)

Question

Calculate the area of the rectangle below using the distributive property.

00:00 Calculate the area of the rectangle

00:03 The area of the rectangle equals side(9+4) multiplied by side(3+2)

00:11 Let's expand the parentheses by multiplying each factor by both terms

00:18 Let's solve each multiplication separately

00:23 Let's add and that's the solution to the problem

The area of a rectangle is equal to its length multiplied by the width.

We begin by writing the following exercise using the data shown in the figure:

$(3+2)\times(9+4)=$

We solve the exercise using the distributive property.

That is:

We multiply the first term of the left parenthesis by the first term of the right parenthesis.

We then multiply the first term of the left parenthesis by the second term of the right parenthesis.

Now we multiply the second term of the left parenthesis by the first term of the left parenthesis.

Finally, we multiply the second term of the left parenthesis by the second term of the right parenthesis.

In the following way:

$(3\times9)+(3\times4)+(2\times9)+(2\times4)=$

We solve each of the exercises within the parentheses:

$27+12+18+8=$

Lastly we solve the exercise from left to right:

$27+12=39$

$39+18=57$

$57+8=65$