Determine what shape is formed for the given coordinates for ABCD, and then find the perimeter and area as an exact value and rounded to the nearest tenth.
(help)

Part 1) The shape is a trapezoid

Part 2) The perimeter is   or approximately  

Part 3) The area is

Step-by-step explanation:

step 1

Plot the figure to better understand the problem

we have

A(-28,2),B(-21,-22),C(27,-8),D(-4,9)

using a graphing tool

The shape is a trapezoid

see the attached figure

step 2

Find the perimeter

we know that

The perimeter of the trapezoid is equal to

the formula to calculate the distance between two points is equal to

Find the distance AB

we have

A(-28,2),B(-21,-22)

substitute in the formula

Find the distance BC

we have

B(-21,-22),C(27,-8)

substitute in the formula

Find the distance CD

we have

C(27,-8),D(-4,9)

substitute in the formula

Find the distance AD

we have

A(-28,2),D(-4,9)

substitute in the formula

Find the perimeter

simplify

----> exact value

therefore

The perimeter is   or approximately  

step 3

Find the area

The area of trapezoid is equal to

substitute the given values

stops on an even number.

< xcy ≅ < xby

step-by-step explanation:

in δcax and δbax,

so, δcax ≅ δbax (side-angle-side or sas)

since δcax ≅ δbax, we can conclude < acx ≅ < abx

in δacy and δaby,

so, δacy ≅ δaby (side-angle-side or sas)

since δacy ≅ δaby, we can conclude < acy ≅ < aby

now,

< acy ≅ < aby

=> < acx + < xcy ≅ < abx + < xby

=> < acx + < xcy ≅ < acx + < xby   (since < acx ≅ < abx already proved above)

subtracting < acx from both sides, we get

< acx + < xcy -< acx ≅ < acx + < xby -< acx

cancelling out < acx and -< acx from both sides, we get

< xcy ≅ < xby (proved)