Question

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1. what is the area of the composite figure?

a) 16 cm²
c) 32 cm²
b) 80 cm²
d) 96 cm²

Explanation:

Step1: Find total area of big rectangle

First, calculate the dimensions of the large rectangle that encloses the figure. The total height is $4+4+4=12$ cm, and the total width is $8$ cm.
Area of big rectangle: $A_{big} = 12 \times 8 = 96$ $\text{cm}^2$

Step2: Find area of white square

The white square has side length $4$ cm.
Area of white square: $A_{white} = 4 \times 4 = 16$ $\text{cm}^2$

Step3: Subtract white area from big area

Subtract the area of the white square from the large rectangle to get the shaded composite area.
$A_{composite} = A_{big} - A_{white} = 96 - 16$

Answer:

b) $80 \text{ cm}^2$