According to the diagram, which of the following statements about area and perimeter of pentagon abcde is true?
a) area = 25 perimeter = 20
b) area = 30 perimeter = 22.31
c) area = 33 perimeter = 12.5
d) area = 35 perimeter = 18

Area = 30 , Perimeter = 22.31 ⇒ Answer (B)

Step-by-step explanation:

* Lets study the figure

- The length of AE = 5

- The length of DC = 3

- The length of BC = 4

- Tho find the length of DE and AB we must use Pythagoras Theorem

∵ The vertical distance of ED = 3 and the horizontal distance = 2

∴ ED = √(3² + 2²) = √13  

- Similar we will find AB

∵ The vertical distance of AB = 6 and the horizontal distance = 3

∴ AB = √(6² + 3²) = √45

* Now we can find its perimeter

- The perimeter = 5 + 4 + 3 + √13 + √45 = 22.31

* to find the area we will divided it into 2 trapezium

- The first one contains E , D , C with point of intersection

 between the vertical axis with side CB

- The lengths of its 2 parallel bases are 3 , 6 and height 2

- The second one contains E , A , B with  point of intersection

 between the vertical axis with side BC

- The lengths of its 2 parallel bases are 2 , 5 and height 6

∵ Area trapezium = (1/2)(b1 + b2) × h

- The area of 1st one = (1/2)(3 + 6) × 2 = 9 units²

- The area of 2nd one = (1/2)(2 + 5) × 6 = 21 units²

∴ The area of the figure = 9 + 21 = 30 units²

* Area = 30 , Perimeter = 22.31

a.   we have two

lines:   y = 4-x   and  

y = 8-x^-1

given two simultaneous equations that are both to be

true, then the solution is the points where the lines cross. the intersection is

where the two equations are equal. therefore the solution that works for both

equations is when

4-x = 8-x^-1

this is where the two lines will cross and that is the

common point that satisfies both equations.

b.   4-x = 8-x^-1

  x           4-x       8-x^-1

-3           7        

8.33

-2           6         8.5

-1           5         9

  0           4        

-

  1           3        

7

  2           2        

7.5

  3           1         7.67

the table shows that none of the x values from -3 to 3 is

the solution because in no case does

4-x = 8-x^-1

to find the solution we need to rearrange the equation to

find for x:

4-x = 8-x^-1

multiply both sides with x:

4x-x^2 = 8x-1

x^2+4x-1=0

x= -4.236, 0.236

therefore there are two points that satisfies the

equation.

find y:  

x=-4.236

y = 4-x   = 4 – (-4.236)

= 8.236

y = 8-x^-1 =   .236)^-1

= 8.236

x=0.236

  y = 4-x   = 4 – (0.236) = 3.764

y = 8-x^-1 =   8-(0.236)^-1

= 3.764

thus the two lines cross at 2 points:

(-4.236, 8.236) & (0.236, 3.764)

c.   to solve

graphically the equation 4-x = 8-x^-1

we would graph both lines: y = 4-x   and   y

= 8-x^-1

the point on the graph where the lines cross is the

solution to the system of equations.

just graph the points on part b on a cartesian coordinate

system and extend the two lines.   the

solution is, as stated, the point where the two lines cross on the graph.

step-by-step explanation:

mark brainliest!