what is the area of the composite figure? (6π + 4) cm² (6π + 16) cm² (12π + 4) cm² (12π + 16) cm² 2 cm

Explanation:

Step1: Analyze the figure's components

The composite - figure consists of a square and four semi - circles. The side length of the square is (2) cm. The four semi - circles can be combined to form two full circles. The radius of each semi - circle (and thus each full circle) is (r = 1) cm.

Step2: Calculate the area of the square

The area formula for a square is (A_{square}=s^{2}), where (s = 2) cm. So (A_{square}=2^{2}=4) (cm^{2}).

Step3: Calculate the area of the two circles

The area formula for a circle is (A=\pi r^{2}), with (r = 1) cm. The area of two circles is (A_{circles}=2\times\pi\times1^{2}=2\pi) (cm^{2}). There are two sets of such circles (top - bottom and left - right), so the total area of the circular parts is (A_{circles\ total}=6\pi) (cm^{2}).

Step4: Calculate the total area of the composite figure

The total area (A = A_{square}+A_{circles\ total}). Substituting the values, we get (A=(6\pi + 4)) (cm^{2}).

Answer:

((6\pi + 4)) (cm^{2})