Exercise 25 Page 62

Before we calculate the perimeter and area, let's draw a diagram of the figure with the given coordinates.

Drawing a Diagram

We will start by plotting the points on a coordinate plane. We can see three sides, so this is a triangle.

We can see that DE is vertical. This observation will help in finding the distance between D and E and also in finding the area of the triangle.

Finding the Perimeter

The perimeter is the sum of the length of the sides. Since DE is vertical, we can find the distance between D and E by counting squares. DE=5 To find the length of the other two sides, we can use the Distance Formula.

DF=sqrt((x_2-x_1)^2+(y_2-y_1)^2)

SubstitutePoints

Substitute ( - 2,- 2) & ( 2,- 1)

DF=sqrt(( 2-( - 2))^2+( - 1-( - 2))^2)

▼

Simplify

SubNeg

a-(- b)=a+b

DF=sqrt((2+2)^2+(- 1+2)^2)

AddTerms

Add terms

DF=sqrt(4^2+1^2)

CalcPow

Calculate power

DF=sqrt(16+1)

AddTerms

Add terms

DF=sqrt(17)

Using the same formula again gives us the distance between E and F. EF=sqrt((2-(- 2))^2+(- 1-3)^2)=sqrt(32) Finally, we can find the perimeter by adding the lengths of the sides. 5+sqrt(32)+sqrt(17)≈ 14.78units

Finding the Area

If we choose the vertical DE as the base of the triangle, then the horizontal segment through F gives the height.

Counting squares again, we can find that the base is b=5 and the height is h=4. Now we can use the formula for the area of a triangle.

A=1/2bh

SubstituteII

b= 5, h= 4

A=1/2( 5)( 4)

Multiply

Multiply

A=10

The area of the triangle is 10units^2.