Question

3
6 cm
1 cm
2 cm
2 cm
3 cm
3 cm
p =
a =

Explanation:

Step1: Calculate the perimeter

The perimeter of a shape is the sum of all its sides. By translating the sides (a common method in geometry for such stepped - like figures), we can find that the perimeter is equivalent to the perimeter of a rectangle with length \(6 + 2+3=11\) cm and width \(1 + 2+3 = 6\) cm.
The formula for the perimeter of a rectangle is \(P=2\times(\text{length}+\text{width})\).

$$P = 2\times(11 + 6)=2\times17 = 34\space\text{cm}$$

Step2: Calculate the area

We can divide the figure into three rectangles.

• The first rectangle (top - left) has dimensions \(6\times1\), and its area \(A_1=6\times1 = 6\space\text{cm}^2\).
• The second rectangle (middle) has dimensions \((6 - 2)\times2=4\times2 = 8\space\text{cm}^2\).
• The third rectangle (bottom - left) has dimensions \(3\times(3 + 2+1)=3\times6 = 18\space\text{cm}^2\).

The total area \(A=A_1+A_2+A_3\).

$$A=6 + 8+18=32\space\text{cm}^2$$

Answer:

\(P = 34\space\text{cm}\), \(A = 32\space\text{cm}^2\)