Question

7 iEstimate the perimeter and the area of the shaded figure to the nearest tenth.perimeter: aboutunitsarea: aboutsquare units

Answer 1

We are asked to determine the perimeter of the given figure. The perimeter is found by adding the length of all the sides of the figure. Taking each square as a unit we divide the figure as follows:

we only need to determine the lengths of the exterior lines of the figure. For figure 1 we have a triangle that has base and height equal to 3 units, therefore, the length of the hypotenuse is:

`h=3\sqrt[]{2}`

Figure 2 is an equal triangle as figure 1. For figure 3 we have 2 units on top and 2 units at the bottom, and for figure 4 we have a circle. The length of the arc of the circle is given by:

`S=\pi r`

Where "r" is the radius. The radius of the circle is 3 units, therefore, the length is:

`S=3\pi`

For this figure we must also add 2 units for the top and 2 units at the bottom. Therefore, the length of each side of the figure is:

`P=3\sqrt[]{2}+2+2+2+3\pi+2+2+2+3\sqrt[]{2}`

Solving the operations:

`P=29.9`

Therfore the perimeter is 29.9 units.

To determine the area we will add the areas of each figure. Figure 1 is a triangle and its area is:

`A_1=(bh)/(2)`

Replacing the values:

`A_1=((3)(3))/(2)=(9)/(2)`

Since figure 2 is an equal triangle we have:

`A_2=(9)/(2)`

For figure 3 the area is the area of a square, that is:

`A_3=2*2=4`

The area of figure 4 is the area of half a circle, that is:

`A_4=(\pi r^2)/(2)`

Replacing:

`A_4=(\pi(3)^2)/(2)=(9)/(2)\pi`

Adding each of the areas:

`\begin{gathered} A=A_1+A_2+A_3+A_4 \\ A=(9)/(2)+(9)/(2)+4+(9)/(2)\pi \end{gathered}`

Solving the operations:

`A=27.1`

Therefore, the area is 27.1 square units.