Find the area of the regular figure below:

A) 466 mm2
B) 430 mm2
C) 404 mm2
D) 495 mm2
E) 512 mm2

explain pls

Option A

Step-by-step explanation:

Central angle of the pentagon =

                                                   =

                                                   = 72°

Measure of ∠BAC = 72°

Therefore, measure of ∠BAD =

                                                 = 36°

By sine rule in ΔABD,

sin(36°) =

            =

            =

BD = 14(sin36°)

     = 8.23 mm

Similarly, by cosine rule,

cos(36°) =

              =

              =

AD = 14(cos36°)

     = 11.33 mm

Area of ΔABC = 2(Area of ΔABD)

                        =

                        = AD × BD

                        = 11.33 × 8.23

                        = 93.21 mm²

Since, area of regular pentagon given in the picture = 5(area of ΔABC)

= 5(93.21)

= 466 mm²

Therefore, Option A will be the answer.

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺