Question

una cartulina rectangular que mide 28 in de largo y 20 in de ancho le han cortado un semi - círculo. ¿cuál es el área restante después de cortar el semicírculo? (utilizar el valor 3.14 para π, y no redondear la respuesta.) 20 in 28 in

Explanation:

1. First, find the area of the rectangle:

• The formula for the area of a rectangle is \(A = l\times w\), where \(l\) is the length and \(w\) is the width.
• Given \(l = 28\) in and \(w = 20\) in.
• So, \(A_{rectangle}=28\times20 = 560\) square - inches.

1. Then, find the area of the semi - circle:

• The diameter of the semi - circle is equal to the width of the rectangle, so \(d = 20\) in, and the radius \(r=\frac{d}{2}=\frac{20}{2}=10\) in.
• The formula for the area of a full - circle is \(A=\pi r^{2}\), and the area of a semi - circle is \(A_{semicircle}=\frac{1}{2}\pi r^{2}\).
• Substitute \(r = 10\) in and \(\pi=3.14\) into the formula for the area of the semi - circle: \(A_{semicircle}=\frac{1}{2}\times3.14\times10^{2}\).
• First, calculate \(10^{2}=100\), then \(\frac{1}{2}\times3.14\times100 = 157\) square - inches.

1. Finally, find the remaining area:

• The remaining area \(A_{remaining}=A_{rectangle}-A_{semicircle}\).
• Substitute \(A_{rectangle}=560\) square - inches and \(A_{semicircle}=157\) square - inches into the formula: \(A_{remaining}=560 - 157=403\) square - inches.

Step1: Calculate rectangle area

\(A_{rectangle}=28\times20 = 560\)

Step2: Calculate semi - circle area

\(A_{semicircle}=\frac{1}{2}\times3.14\times10^{2}=157\)

Step3: Calculate remaining area

\(A_{remaining}=560 - 157\)

Answer:

403