Question

find the area of each figure, round your answer to one decimal pla
compound shapes
1)
18 cm
18 cm
18 cm
30 cm
area: 864 cm²
a =
b =
shaded =
2)
16 cm
8 cm
8 cm
28 cm
area: 384 cm²
a_a =
a_b =
a_shaded =
5 cm
11 cm
6 cm
15 cm
5)
4 cm
8 cm
4 cm
8 cm

Explanation:

Step1: Analyze Figure 1 (T - shape)

The T - shape can be divided into two rectangles. The top rectangle has dimensions \(18\space cm\times18\space cm\), and the bottom rectangle has dimensions \(30\space cm\times18\space cm\).
Area of top rectangle (\(A_1\)): \(A_1 = 18\times18=324\space cm^2\)
Area of bottom rectangle (\(A_2\)): \(A_2=30\times18 = 540\space cm^2\)
Total area (\(A\)): \(A=A_1 + A_2=324 + 540=864\space cm^2\)

Step2: Analyze Figure 2 (Rectangle with a square cut - out)

The large rectangle has dimensions \(28\space cm\times16\space cm\), and the square cut - out has dimensions \(8\space cm\times8\space cm\).
Area of large rectangle (\(A_A\)): \(A_A=28\times16 = 448\space cm^2\)
Area of square cut - out (\(A_B\)): \(A_B = 8\times8=64\space cm^2\)
Shaded area (\(A_{shaded}\)): \(A_{shaded}=A_A - A_B=448 - 64 = 384\space cm^2\)

Step3: Analyze the rectangle - in - rectangle figure (bottom left)

The outer rectangle has dimensions \(15\space cm\times6\space cm\), and the inner rectangle has dimensions \(11\space cm\times5\space cm\).
Area of outer rectangle (\(A_{outer}\)): \(A_{outer}=15\times6 = 90\space cm^2\)
Area of inner rectangle (\(A_{inner}\)): \(A_{inner}=11\times5 = 55\space cm^2\)
Shaded area (\(A_{shaded}\)): \(A_{shaded}=A_{outer}-A_{inner}=90 - 55 = 35\space cm^2\)

Step4: Analyze Figure 5 (Square with a square cut - out)

The outer square has side length \(8\space cm\), and the inner square has side length \(4\space cm\).
Area of outer square (\(A_{outer}\)): \(A_{outer}=8\times8 = 64\space cm^2\)
Area of inner square (\(A_{inner}\)): \(A_{inner}=4\times4 = 16\space cm^2\)
Shaded area (\(A_{shaded}\)): \(A_{shaded}=A_{outer}-A_{inner}=64 - 16 = 48\space cm^2\)

Answer:

For Figure 1: Area = \(864\space cm^2\)
For Figure 2: \(A_A = 448\space cm^2\), \(A_B = 64\space cm^2\), \(A_{shaded}=384\space cm^2\)
For the bottom - left figure: \(A_{shaded}=35\space cm^2\)
For Figure 5: \(A_{shaded}=48\space cm^2\)