Chapter 1.6, Problem 25PPS

To determine

To graph and identify the figure and find perimeter and area

Answer to Problem 25PPS

Perimeter is 14.77 units.

Area is 8.65 $uni{t}^2$ .

Explanation of Solution

Given information:

  $D(-2,-2),E(-2,3),F(2,-1)$

Formula used:

  $S=\sqrt{s(s-a)(s-b)(s-c)}$

  $s=\frac{a+b+c}{2}$

Where a, b, c is sides

Graph:

  

Interpretation:

The given figure is a triangle.

Calculation:

To find the perimeter and area, find out the length of each vertices.

Substituting values distance formula,

  $DE=\sqrt{{(-2+(-2))}^2+{(3-(-2))}^2}$

Solving,

  $DE=\sqrt{{(0)}^2+{(5)}^2}$

So,

  $DE=5$

Similarly,

  $EF=\sqrt{{(2-(-2))}^2+{(-1-3)}^2}$

Solving,

  $EF=\sqrt{{(4)}^2+{(-4)}^2}$

So,

  $EF=4\sqrt{2}$

Similarly,

  $FD=\sqrt{{(-2-2)}^2+{(-1-(-2))}^2}$

Solving,

  $FD=\sqrt{{(-4)}^2+{(1)}^2}$

So,

  $FD=\sqrt{17}$

Perimeter is sum of all sides.

So,

perimeter= $5+4\sqrt{2}+\sqrt{17}$ =14.77 units

Hence, perimeter is 14.77 units.

Now,

Area using heron’s formula,

  $S=\sqrt{s(s-a)(s-b)(s-c)}$

  $s=\frac{a+b+c}{2}$

Substituting values

  $s=\frac{5+4\sqrt{2}+\sqrt{17}}{2}$

Solving,

  $s=7.2$

Now,

  $S=\sqrt{7.2(7.2-5)(7.2-4\sqrt{2})(7.2-\sqrt{17})}$

Solving,

  $S=\sqrt{7.2(2.2)(1.54)(3.07)}$

Multiplying,

  $S=\sqrt{74.88}$

Rooting,

  $S=8.65uni{t}^2$

Hence area is 8.65 $uni{t}^2$ .