Find areas by decomposing into rectangles and composite figures

Find area by decomposing into rectangles or completing composite figures to form rectangles.

Addy finds the area of a 5-inch by 17-inch rectangle by breaking it

into 2 smaller rectangles. Show one way that he could have

solved the problem. What is the area of the rectangle?

How can we find the area?

17 in.

​

​5 in.

We can decompose the rectangle!

Step 1 - cut the larger number into two numbers that are easier to multiply by.
Step 2 - multiply both new numbers by the number that stayed the same.
Step 3 - add the products together.

​

​5 in.

10 in.

7 in.

Multiple Choice

What is the product of 5 and 10?

• 50

• 5

• 10

• 150

Multiple Choice

What is the product of 5 and 7?

• 5

• 35

• 7

• 37

Multiple Choice

If 5 x 10 = 50 and 5 x 7 = 35 then what is the sum of those two products?

• 80

• 85

• 90

• 95

Multiple Choice

What is the area of this figure?

• 80 in. squ.

• 75 in. squ.

• 85 in. squ.

• 90 in. squ.

We can decompose the rectangle!

Step 1 - cut the larger number into two numbers that are easier to multiply by.
Step 2 - multiply both new numbers by the number that stayed the same.
Step 3 - add the products together.

​

​5 in.

10 in.

7 in.

​5 x 10 = 50
5 x 7 = 35
50 + 35 = 85 in. squ.

Multiple Choice

Find the area.

• 80 in squ

• 114 in squ

• 120 in squ

• 132 in squ

How can we find the area?

We can compose the shape!

Step 1 - Draw to complete the rectangle.
Step 2 - multiply rows by columns
Step 3 - subtract the number of blank/white pieces.

Multiple Choice

Which multiplication sentence can I use to find the area?

• 3 x 4

• 6 x 2

• 4 x 4

• 4 x 3

Multiple Choice

4 x 4 = ?

• 4

• 16

• 12

• 97

Multiple Choice

Which number sentence completes the composed figure equation?

16 - ? = ?

• 16 - 5 = ?

• 16 - 4 = ?

• 16 - 3 = ?

• 16 - 2 = ?

Multiple Choice

What is the area of the figure?

• 16 units squ.

• 12 units squ.

• 10 units squ.

• 9 units squ.

We can compose the shape!

Step 1 - Draw to complete the rectangle.
Step 2 - multiply rows by columns
Step 3 - subtract the number of blank/white pieces.

​4 x 4 = 16
16 - 4 = 12
12 units squ.

Multiple Choice

Find the area.

• 4 x 5 = 25

  25 - 5 = 20

  20 units squ.

• 5 + 5 = 10

  10 + 10 = 20

  20 units squ.

• 5 x 4 = 20

  20 - 6 = 14

  14 units squ.

• 4 x 4 = 16

  16 - 6 = 10

  10 units squ.

How can we find the are?

How can we find the are?

​5

​4

How can we find the are?

​5

​7

​9

​63

​4

How can we find the are?

​5

​7

​9

​63

​5

​4

​4

​20

How can we find the are?

​5

​7

​9

​63

​5

​4

​4

​20

​63 - 20 = 43 squ cm.

The next 4 questions are for you and your table

Multiple Choice

What is the total area of A and B?

• 42 units squ

• 36 units squ

• 27 units squ

• 18 units squ

Multiple Choice

Find the total area of C and D

• 42 units squ

• 27 units squ

• 35 units squ

• 33 units squ

Multiple Choice

Find the total area of E and F

• 19 units squ

• 30 units squ

• 21 units squ

• 27 units squ

Multiple Choice

Find the area of only the shaded figure.

• 12 cm squ

• 90 cm squ

• 78 cm squ

• 102 cm squ