Answer: 264 cm²
Step-by-step explanation:
The composite figure is formed by: A square, a trapezium and a rectangle.
The area of the composite figure is the sum of the areas of: the square, the trapezium and the rectangle.
The formula for calculate the area of a square is:
[tex]A_s=s^2[/tex]
Where s is the side lenght.
The side lenght of the square in the figure is:
[tex]s=10cm[/tex]
The formula for calculate the area of a trapezium is:
[tex]A_t=(\frac{B+b}{2})h[/tex]
Where B is the larger base, b is the smaller base and h is the height.
The dimensions of the trapezium of the figure are:
[tex]B=20cm-4cm-2cm=14cm\\b=5cm+3cm=8cm\\h=4cm[/tex]
The formula for calculate the area of a rectangle is:
[tex]A_r=lw[/tex]
Where w is the width and l is the length.
The dimensions of the rectangle of the figure are:
[tex]l=20cm\\w=6cm[/tex]
Therefore, substituting values, you obtain the following result:
[tex]A_{cf}=(10cm)^2+(\frac{14cm+8cm}{2})4+(20cm*6cm)=264cm^2[/tex]
