Part 1: What is the sum of the perimeters, in units, of the five squares in the design? Round your answer to the nearest tenth.

Part 2: What is the sum of the areas, in square units, of the five squares in the design? Round your answer to the nearest whole unit.

We want to get the total perimeter and area of the 5 graphed squares, we will get:

Remember that for a square of sidelength s, the perimeter is:

P = 4*s

And the area is:

A = s^2

In the graph, we can see 4 small squares with sidelength s = 3

We have a larger square with a diagonal equal to 8 units.

The relation between the diagonal and the sidelength is:

D = s*√2

Then the sidelength of the larget square is:

s = 8/√2

a) The sum of the perimeters of the 5 squares is:

P = 4*(4*3) + 4*8/√2 = 70.627 units

b) The sum of the areas of the 5 squares is:

A = 4*(3^2) + (8/√2)^2 = 68 units squared.

If you want to learn more, you can read:

link

Part 1: Perimeter of the 5 squares = 64 units

Part 2: Area of the 5 squares = 52 units²

Step-by-step explanation:

We have four similar squares and one bigger square in the design.

Part 1:

Perimeter of the 5 squares = 4 * Perimeter of each little square + Perimeter of the big square

We can notice that each side of each little square is 3 units and the side of the big square is 4 units, in consequence we have:

Perimeter of the 5 squares = 4 * (3 + 3 + 3 + 3) + (4 + 4 + 4 + 4)

Perimeter of the 5 squares = 4 * 12 + 16

Perimeter of the 5 squares = 64 units

Part 2:

Area of the 5 squares = 4 * Area of each little square + Area of the big square

We can notice that each side of each little square is 3 units and the side of the big square is 4 units, in consequence we have:

Area of the 5 squares = 4 * (3²) + (4²)

Area of the 5 squares = 36 + 16

Area of the 5 squares = 52 units²