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

75 tickets have been sold so far.

step-by-step explanation:

in this question it is clearly mentioned that 45 children's tickets have been sold and this number is 60% of the total tickets sold.

now let's assume the total number of tickets sold be x.

then 60% of x = 45

⇒

⇒ x(.6) = 45

by dividing with .6 on both the sides of the equation

⇒ x = 75

therefore 75 tickets have been sold so far.