Question

find the area of the shape. (sides meet at right angles.)

Explanation:

Step1: Divide the shape

Divide the given shape into three rectangles.

Step2: Calculate the area of each rectangle

• For the left - most rectangle: length $l_1 = 6\ \text{cm}$, width $w_1=2\ \text{cm}$. Area $A_1=l_1\times w_1=6\times2 = 12\ \text{cm}^2$.
• For the middle - upper rectangle (which is a square as length = width = 2 cm): Area $A_2 = 2\times2=4\ \text{cm}^2$.
• For the middle - lower rectangle (which is a square as length = width = 2 cm): Area $A_3 = 2\times2 = 4\ \text{cm}^2$. But wait, we can also use another approach.

Another way: The total shape can be thought of as a combination where we can calculate the area as follows. The base of the large - like structure: the total horizontal length is $2 + 2+2=6\ \text{cm}$ (but no, correct approach).
Correct approach:
The area of the shape can be calculated as:
The area of the big rectangle (height = 6 cm, width = 2 cm) plus the area of the square (side = 2 cm)

$$A=(2\times6)+(2\times2)$$

$$A = 12 + 4$$

$$A=16\ \text{cm}^2$$

Answer:

$16\ \text{cm}^2$