Question

which composite figure has the greatest surface area?

Explanation:

Step1: Calculate surface area of first figure

Assume the side - length of the basic cube - like parts. For the first composite figure, we can use the method of counting or calculating the area of each face. If we consider the standard formula for the surface area of a composite 3D - shape (by adding up the areas of all outer - facing faces). Let's assume each small square face has an area of \(1\times1 = 1\) (if we consider the unit as 1). The first figure has a surface area calculation:

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Step2: Calculate surface area of second figure

For the second composite figure, using the formula for the surface area of a rectangular prism \(S = 2(ab+bc + ac)\) where \(a = 2\), \(b=2\), \(c = 3\) (by combining the two parts).

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Step3: Calculate surface area of third figure

The third figure is a cube with side - length \(a = 2\). The surface area formula of a cube is \(S=6a^{2}\). Substituting \(a = 2\) into the formula:

$$S = 6\times2^{2}=6\times4 = 24$$

Step4: Calculate surface area of fourth figure

For the fourth composite figure, we use the method of counting or calculating the area of each face.

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Answer:

The first, second and fourth composite figures have the greatest surface area.