Multiply 2 two digit numbers using an area model
We've seen how to multiply a two digit number by another two digit number. Now we are going to apply that to area.
$\text{Area of a rectangle }=\text{length }\times\text{width }$Area of a rectangle =length ×width
So if we had a length of $18$18 and a width of $42$42 we would get an equation that looks like this.
$\text{Area }=18\times42$Area =18×42
Rather than trying to add up forty two $18$18s in our head, it is much simpler to break the area up into smaller parts, multiply them separately and then add them all together to get the total area.
This video here will help you see what to do.
Worked Examples
Question 1
Calculate $10\times18$10×18 by completing an area model.
Firstly, complete the missing values in the area model.
x $10$10 $10$10 $\editable{}$ $8$8 $\editable{}$ Now add the values you found in part a to calculate $10\times18$10×18.
Question 2
Calculate $26\times39$26×39 by completing an area model.
Firstly, complete the missing values in the area model.
x $20$20 $6$6 $30$30 $\editable{}$ $\editable{}$ $9$9 $\editable{}$ $\editable{}$ Now add the values you found in part a to calculate $26\times39$26×39.
Question 3
Use the area model to find $77\times69$77×69.
Fill in the areas of each rectangle.
$70$70 $7$7 $60$60 $\editable{}$ $\editable{}$ $9$9 $\editable{}$ $\editable{}$ What is the total area of all four rectangles?
So what is $77\times69$77×69?