Question

question 2: determine laire et le périmètre des figures suivantes a)

Explanation:

Step1: Analyze the figure

The figure is a rectangle with a quarter - circle cut out. The rectangle has length \(l = 20\) cm and width \(w=20\) cm. The radius of the quarter - circle \(r = 10\) cm.

Step2: Calculate the area of the rectangle

The area of a rectangle \(A_{rect}=l\times w\). So \(A_{rect}=20\times20 = 400\) \(cm^{2}\).

Step3: Calculate the area of the quarter - circle

The area of a full - circle is \(A_{circle}=\pi r^{2}\), and for a quarter - circle \(A_{q - circle}=\frac{1}{4}\pi r^{2}\). Substituting \(r = 10\) cm, we get \(A_{q - circle}=\frac{1}{4}\pi\times(10)^{2}=25\pi\) \(cm^{2}\approx 25\times 3.14 = 78.5\) \(cm^{2}\).

Step4: Calculate the area of the figure

\(A = A_{rect}-A_{q - circle}=400 - 25\pi\approx400-78.5 = 321.5\) \(cm^{2}\).

Step5: Calculate the perimeter of the rectangle part

The perimeter of the rectangle part that contributes to the figure's perimeter: two sides of length \(20\) cm and one side of length \(10\) cm. So \(P_{rect}=2\times20 + 10=50\) cm.

Step6: Calculate the arc - length of the quarter - circle

The arc - length of a quarter - circle \(s=\frac{1}{4}\times2\pi r\). Substituting \(r = 10\) cm, we get \(s = 5\pi\) cm\(\approx5\times3.14 = 15.7\) cm.

Step7: Calculate the perimeter of the figure

\(P=P_{rect}+s=50 + 5\pi\approx50+15.7 = 65.7\) cm.

Answer:

Area: \(400 - 25\pi\approx321.5\) \(cm^{2}\), Perimeter: \(50 + 5\pi\approx65.7\) cm