Question

perimeter, circumference, and area assignment part 1

1. find the area of the shaded region.
2. find the area of the shaded region.

Explanation:

Step1: Calculate outer - shape area for the first problem

The outer - shape is a rectangle with length $l = 14$ in and width $w = 11$ in. The area formula for a rectangle is $A = l\times w$. So, $A_{outer1}=14\times11 = 154$ in².

Step2: Calculate inner - shape area for the first problem

The inner - shape is a rectangle with length $l = 10$ in and width $w = 9$ in. The area formula for a rectangle is $A = l\times w$. So, $A_{inner1}=10\times9 = 90$ in².

Step3: Calculate shaded area for the first problem

The shaded area $A_{1}$ is the difference between the outer and inner areas. $A_{1}=A_{outer1}-A_{inner1}=154 - 90=64$ in².

Step4: Calculate outer - shape area for the second problem

The outer - shape is a square with side length $s = 20$ km. The area formula for a square is $A = s^{2}$. So, $A_{outer2}=20\times20 = 400$ km².

Step5: Calculate inner - shape area for the second problem

The inner - shape is a circle with radius $r = 10$ km. The area formula for a circle is $A=\pi r^{2}$. So, $A_{inner2}=\pi\times(10)^{2}=100\pi$ km².

Step6: Calculate shaded area for the second problem

The shaded area $A_{2}$ is the difference between the outer and inner areas. $A_{2}=A_{outer2}-A_{inner2}=400 - 100\pi\approx400-100\times3.14 = 400 - 314=86$ km².

Answer:

1. $64$ in²
2. $(400 - 100\pi)\text{ km}^2\approx86$ km²