Question

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

Explanation:

Step1: Calculate area of the square

The side - length of the square is \(a = 4\) cm (since \(2\times2\)). The area formula of a square is \(A_{square}=a^{2}\). So \(A_{square}=4^{2}=16\) \(cm^{2}\).

Step2: Calculate area of the semi - circles

There are 4 semi - circles of the same radius \(r = 2\) cm. The 4 semi - circles are equivalent to 2 full - circles. The area formula of a circle is \(A=\pi r^{2}\), with \(r = 2\) cm. So \(A_{circles}=2\times\pi\times2^{2}=8\pi\) \(cm^{2}\), and there are 2 more semi - circles with radius \(r = 2\) cm which have an area of \(4\pi\) \(cm^{2}\), and the total area of all circular parts is \(12\pi\) \(cm^{2}\).

Step3: Calculate the area of the composite figure

The area of the composite figure \(A = A_{square}+A_{circles}\). So \(A=(12\pi + 16)\) \(cm^{2}\).

Answer:

\((12\pi + 16)\) \(cm^{2}\)