Question

3.) a.) Explain how to decompose the large rectangle and figure 12.4 into 2 1/2 groups with 3 1/2 squares in each group, so as to describe the area of the rectangle as 2 1/2×3 1/2 cm² b.) calculate 2 1/2×3 1/2 without a calculator, showing your calculations. Then verify that this calculation has the same answer as when you determine the area of the rectangle and bigger 12.4 by counting squares

Answer 1

Part A

The large rectangle has been divided into squares with an area of 1 cm square each as the benchmark.

If we observe:

• There are 6 green squares with an area of 1 cm square each.

,

• There are 5 blue rectangles with an area of 1/2 cm square each.

,

• There is a white square with an area of 1/4 square cm.

Therefore, the area of the rectangle

=(6 x 1)+(5 x ½) + ¼

=6 + 2.5 + 0.25

=8.75 cm²

Part B

Next, we calculate 2½ × 3½.

2½ x 3½ = 5/2 x 7/2

=35/4

=8.75 cm²

This calculation has the same answer as to when you determine the area of the rectangle by counting squares.