Question

1. what is the area of the unshaded part in the figure below? a. 154 cm² b. 56 cm² c. 112 cm² d. 98 cm²

Explanation:

Step1: Calculate the area of the square

The area of a square is \(A = s^2\), where \(s = 14\) cm. So \(A_{square}=14\times14 = 196\) \(cm^{2}\).

Step2: Calculate the area of a quarter - circle

The area of a circle is \(A=\pi r^{2}\), for a quarter - circle \(A_{quarter - circle}=\frac{1}{4}\pi r^{2}\), with \(r = 14\) cm and \(\pi=\frac{22}{7}\). Then \(A_{quarter - circle}=\frac{1}{4}\times\frac{22}{7}\times14\times14=\frac{1}{4}\times22\times2\times14 = 154\div2= 77\) \(cm^{2}\).

Step3: Calculate the area of one shaded part

The area of one shaded part \(A_{one - shaded}=A_{square}-A_{quarter - circle}\). So \(A_{one - shaded}=196 - 77=119\) \(cm^{2}\) (This step was wrong, let's correct: The area of the un - shaded part: The sum of two quarter - circles (a semi - circle) minus the square. The area of a semi - circle \(A_{semi - circle}=\frac{1}{2}\pi r^{2}=\frac{1}{2}\times\frac{22}{7}\times14\times14= 308\) \(cm^{2}\).)

Step4: Calculate the area of the un - shaded part

\(A_{un - shaded}=A_{semi - circle}-A_{square}\). \(A_{un - shaded}=\frac{1}{2}\times\frac{22}{7}\times14\times14-14\times14\). \(A_{un - shaded}=308 - 196=112\) \(cm^{2}\).

Answer:

C. \(112\ cm^{2}\)