 Decompose a shape into rectangles to find the area

Lesson

By breaking a shape into smaller rectangles, we can work out the area of those rectangles first. We can then add those two values together, to work out the total area of our shape.

Worked Examples

Question 1

The total area of this shape is $37$37 cm2.

If the area of rectangle $A$A is $15$15 cm2, what is the area of rectangle $B$B?

 $A$A $B$B

Question 2

Find the area of the given shape.

 $5$5 cm $\uparrow$↑ $5$5 cm $\downarrow$↓ $4$4 cm $9$9 cm

Question 3

Find the area of the given shape. Outcomes

5.M2.05

Determine, through investigation using a variety of tools (e.g., concrete materials, dynamic geometry software, grid paper) and strategies (e.g., building arrays), the relationships between the length and width of a rectangle and its area and perimeter, and generalize to develop the formulas [i.e., Area = length x width; Perimeter = (2 x length) + (2 x width)]

5.M2.06

Solve problems requiring the estimation and calculation of perimeters and areas of rectangles