Question Video: Using an Area Model to Deduce the Distributive Property of Multiplication | Nagwa Question Video: Using an Area Model to Deduce the Distributive Property of Multiplication | Nagwa

Question Video: Using an Area Model to Deduce the Distributive Property of Multiplication Mathematics

The diagram shows a rectangle of sides π and π + π. Its area is thus π Γ (π Γ π), also written as π(π + π). Work out the area of the two rectangles that make up the bigger rectangle to find an equivalent expression to π(π + π).

01:49

Video Transcript

The diagram shows a rectangle of sides π and π plus π. Its area is thus π times parenthesis π times π parenthesis, also written as π parenthesis π plus π parenthesis. Work out the area of the two rectangles that make up the bigger rectangle to find an equivalent expression to π times parenthesis π plus π parenthesis.

So here we have side π and side π plus π of this larger triangle. The area of a rectangle is equal to length times width. So for the entire rectangle, its area would be π times π plus π, which can also be written as π parenthesis π plus π parenthesis.

Now weβre told to work out the area of the two rectangles that make up the bigger rectangle. So we have this one and this one. So letβs look at the striped one first. Its area will be π times π, which could also just be written as ππ.

Now the polka dot rectangle, this length must also be π. So its length times width formula, weβll actually be also be using the same π. So its area would be π times π, or ππ.

So to have the area of the entire rectangle, we will just need to add these areas together. So we would have ππ plus ππ. And this should make sense because if we would distribute the π to the π plus π, we would have π times π, which is ππ, plus π times π. And thatβs what we have: ππ plus ππ. So this will be our final answer.

Join Nagwa Classes

Attend live sessions on Nagwa Classes to boost your learning with guidance and advice from an expert teacher!

• Interactive Sessions
• Chat & Messaging
• Realistic Exam Questions