Answer:
73 cm²
Step-by-step explanation:
Areas and volumes of composite figures are found by dividing the figure into shapes you have formulas for. Sometimes that will be a sum of shapes, and sometimes it will involve the difference of shapes.
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setup
This shape can be decomposed into two rectangles by extending the horizontal line. (This is the dashed line shown in the attachment.)
The width of the top rectangle will be the sum of the lengths of the labeled horizontal segments:
4 cm + 5 cm + 3 cm = 12 cm
The height of the top rectangle, and the dimensions of the bottom rectangle (square) are shown in the given figure.
The area of each rectangle is the product of its width and height.
A = WH
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solution
top rectangle area = WH = (12 cm)(4 cm) = 48 cm²
bottom rectangle area = WH = (5 cm)(5 cm) = 25 cm²
Area = top rectangle area + bottom rectangle area = (48 cm²) +(25 cm²)
Area = 73 cm²
The area of this composite shape is 73 cm².
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Additional comment
The figure will fit into a rectangle that is 9 cm high by 12 cm wide. From that rectangle, a rectangle 5 cm high and 4 cm wide is removed from the lower left, and a rectangle 5 cm high and 3 cm wide is removed from the lower right. Figuring the area this way, we find it to be ...
figure area = bounding rectangle area - removed areas
= (9 cm)(12 cm) -(5 cm)(4 cm) -(5 cm)(3 cm) = 108 cm² -20 cm² -15 cm²
= 73 cm²
