The problem asks to find the area and perimeter of the six composite shapes shown in the image. I will solve the first one, labeled 1). The shape is a rectangle with a smaller rectangle removed from the top. The given dimensions are: height of left side is 43 cm, bottom width is 44 cm, height of the two vertical lines at the top are 30 cm, the width of the top removed rectangle is 26 cm.

1. Problem Description

The problem asks to find the area and perimeter of the six composite shapes shown in the image. I will solve the first one, labeled 1). The shape is a rectangle with a smaller rectangle removed from the top. The given dimensions are: height of left side is 43 cm, bottom width is 44 cm, height of the two vertical lines at the top are 30 cm, the width of the top removed rectangle is 26 cm.

2. Solution Steps

Area Calculation:

The overall shape looks like a large rectangle with a smaller rectangle cut out from the top.

First find the dimensions of the larger rectangle:

Height = 43 cm

Width = 44 cm

Area of the larger rectangle, $A_1 = \text{height} \times \text{width} = 43 \times 44 = 1892 \text{ cm}^2$

Now find the dimensions of the smaller (removed) rectangle:

Height = 30 cm

Width = 26 cm

Area of the smaller rectangle, $A_2 = \text{height} \times \text{width} = 30 \times 26 = 780 \text{ cm}^2$

The area of the composite shape, $A = A_1 - A_2 = 1892 - 780 = 1112 \text{ cm}^2$

Perimeter Calculation:

The perimeter is the sum of the lengths of all the sides.

The outer shape has two sides of length 43 cm and one side of length 44 cm.

The inner shape has two sides of length 30 cm and one side of length 26 cm.

The remaining sides on the bottom are $44-26 = 18$cm total, because there are two segments each of length 9cm (since the cutout is centered).

Perimeter $P = 43 + 43 + 44 + 30 + 30 + 26 = 216$ cm.

3. Final Answer

Area = 1112 cm^2

Perimeter = 216 cm