Question

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

Explanation:

Step1: Divide the figure into two rectangles

We can split the composite figure into two rectangles. One rectangle has dimensions \( 7 \, \text{cm} \) (length) and \( 3 \, \text{cm} \) (height). The other rectangle has dimensions \( (7 - 3) \, \text{cm}=4 \, \text{cm} \) (length) and \( (6 - 3) \, \text{cm} = 3 \, \text{cm}\) (height).

Step2: Calculate the area of the first rectangle

The area of a rectangle is given by the formula \( A = l \times h \), where \( l \) is the length and \( h \) is the height. For the first rectangle with \( l = 7 \, \text{cm} \) and \( h=3 \, \text{cm} \), the area \( A_1=7\times3 = 21 \, \text{cm}^2 \).

Step3: Calculate the area of the second rectangle

For the second rectangle with \( l = 4 \, \text{cm} \) and \( h = 3 \, \text{cm} \), the area \( A_2=4\times3=12 \, \text{cm}^2 \).

Step4: Sum the areas of the two rectangles

To find the total area of the composite figure, we add the areas of the two rectangles: \( A = A_1+A_2=21 + 12=33 \, \text{cm}^2 \).

Answer:

The area of the figure is \( 33 \, \text{cm}^2 \).