Me! how do i find the area of the shaded region in the circles?

Step-by-step explanation:

10a)

The formula for determining the area of a sector is expressed as

Area = #/360 × πr^2

From the diagram given,

# = π/3. We would convert π to degrees. 2π = 360 degrees. It means that π = 360/2 = 180 degrees. Therefore

π/3 = 180/3 = 60 degrees.

r = 10

Area of sector = 60/360 × 3.14 × 10^2 = 52.33 cm^2

Area of the triangle formed can be determined by the formula,

Area = 1/2abSinC

From the triangle,

a = 10,

b = 10

C = π/3 = 60 degrees. Therefore,

Area = 1/2 × 10 × 10 × Sin60 = 50 × 0.8660

Area of triangle = 43.3 cm^2

Therefore, area of the shaded region would be

53.3 - 43.3 = 10 cm^2

10b) looking at the diagram,

# = 135 degrees

r = 12

Area of sector = 135/360 × 3.14 × 12^2 = 169.56 cm^2

Area of the triangle = 1/2 × 12 × 12 × Sin 135 = 1/2 × 144 × 0.7071 = 50.9 cm^2. Therefore, the area of the shaded region would be

169.56 - 50.9 = 114.66 cm^2

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 ☺

b. hannah is playing with her cousin at