Question

find the area of each shape. include 1. 10 cm 5 cm 8 cm 6 cm 3 cm 4 cm 3. 1 m 4 m 4 m 4 m 4 m 5 m 5 m

Explanation:

Step1: Divide the shape into rectangles

For the first - given shape:
We can divide the complex shape into two rectangles. The first rectangle has dimensions \(5\times3\) and the second rectangle has dimensions \((7 - 3)\times(5 - 2)=4\times3\).
For the second - given shape:
We can divide it into three rectangles. Let's consider the rectangles with dimensions:
Rectangle 1: \(5\times(10 - 6)=5\times4\)
Rectangle 2: \(3\times6\)
Rectangle 3: \(8\times4\)
For the third - given shape:
We can divide it into three rectangles. Rectangle 1: \(4\times1\), Rectangle 2: \(4\times(4 + 1)=4\times5\), Rectangle 3: \(5\times(4 + 4)=5\times8\)

Step2: Calculate the area of each rectangle

First shape:

Area of rectangle 1 \(A_1 = 5\times3=15\space m^2\)
Area of rectangle 2 \(A_2=(7 - 3)\times(5 - 2)=4\times3 = 12\space m^2\)
Total area \(A=A_1 + A_2=15 + 12=27\space m^2\)

Second shape:

Area of rectangle 1 \(A_1 = 5\times4 = 20\space cm^2\)
Area of rectangle 2 \(A_2=3\times6 = 18\space cm^2\)
Area of rectangle 3 \(A_3=8\times4 = 32\space cm^2\)
Total area \(A=A_1+A_2 + A_3=20 + 18+32=70\space cm^2\)

Third shape:

Area of rectangle 1 \(A_1 = 4\times1=4\space m^2\)
Area of rectangle 2 \(A_2=4\times5 = 20\space m^2\)
Area of rectangle 3 \(A_3=5\times8 = 40\space m^2\)
Total area \(A=A_1+A_2 + A_3=4 + 20+40=64\space m^2\)

Answer:

The areas of the three shapes are \(27\space m^2\), \(70\space cm^2\), and \(64\space m^2\) respectively.