Question

What is the area of the composite figure?

Answer 1

Answer: 264 cm²

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:

`A_s=s^2`

Where s is the side lenght.

The side lenght of the square in the figure is:

`s=10cm`

The formula for calculate the area of a trapezium is:

`A_t=((B+b)/(2))h`

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:

`B=20cm-4cm-2cm=14cm\\b=5cm+3cm=8cm\\h=4cm`

The formula for calculate the area of a rectangle is:

`A_r=lw`

Where w is the width and l is the length.

The dimensions of the rectangle of the figure are:

`l=20cm\\w=6cm`

Therefore, substituting values, you obtain the following result:

`A_(cf)=(10cm)^2+((14cm+8cm)/(2))4+(20cm*6cm)=264cm^2`