The expressions for each area are: 28x²-35x ( rectangle ), 9x² ( square ) and 37x²-35x ( total area )
Area of Compound Shapes
This exercise requires your knowledge about the area of compound shapes. For solving this, you should:
- Identify the basic shapes;
- Calculate your individual areas;
- Sum each area found.
- STEP 1 - Identify the basic shapes.
The figure is composed of a square and a rectangle. See the attached image.
Therefore, you should sum the area of these geometric figures for determining the area of the irregular figure.
- STEP 2 - Find the area of the rectangle.
Area of the rectangle = bh . The figure shows that the sides for this rectangle are equal to 4x-5 and (4x+3x). Then,
b= length of the base= 4x-5
h=height=4x+3x=7x
Thus, A_rectangle=bh= (4x-5)*7x=28x²-35x
- STEP 3 - Find the area of the square.
Area of the square= l². The figure shows that the sides for this square are equal to 3x
l= length of the side= 3x
Thus, A_square=l²= (3x)² =9x²
- STEP 4 - Find an expression for the total area of the figure.
A_total= A_rectangle+A_square
A_total= 28x²-35x+9x²
A_total= 37x²-35x
Learn more about the area of compound shapes here:
https://brainly.com/question/15884960
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