# Grades 10 to 12 Expansion of brackets. Area and quadratic equations.

*By Kwethemba Moyo On 15 August, 2019 · Leave a Comment*

Find the area of a rectangle whose dimensions are: (*2x + 3*) by (*x + 1*).

Sketch and label the rectangle whose dimensions are: (*2x* *+ 3*) by (*x + 1*)

How do we calculate the area of a rectangle?

Can partitioning (subdividing) the rectangle into simpler units help us? Find the areas of these sub-units.

What is the total area obtained from the subdivided rectangle?

Can the rectangle be further subdivided into simpler squares and rectangles? Try this out.

What do you obtain as the area of the original rectangle?

How else would you have obtained this area without subdividing the rectangle?

Can you multiply (*2x* *+ 3*) by (*x + 1*)?

Does your method yield the same results?

If the numerical value of the area of the rectangle is given as 21 square units, form an equation in terms of *x. *Hence solve it to find the dimensions of the rectangle.

Does the area of the rectangle equal 21 square units? Check the validity of your solutions.

On a Cartesian plane, sketch the graphs of each of the functions you formed.

What are the x-intercepts of the graphs? What do you notice between these vales and the solutions you obtained above?

Using the same method or otherwise, find the area of a rectangle whose dimensions are: (*2x + 1*)(*x + 2). *

If the numerical value of the area of this rectangle is 5 square units. Find the dimensions of the rectangle.

Click here for notes for teachers.

### Login

### SUPPORT AIMSSEC