Find the area of the shaded region.

approximately 33.59 square cm

Work Shown:

P = area of equilateral triangle with side length 's'

P = (sqrt(3)/4)*s^2

P = (sqrt(3)/4)*14^2

P = 49*sqrt(3)

Q = area of circle with radius r

Q = pi*r^2

Q = pi*4.04^2

Q = 16.3216pi

S = area of shaded region

S = P - Q

S = 49*sqrt(3) - 16.3216pi

S = 33.5946709160439

S = 33.59

33.6 cm² (3 sf)

Step-by-step explanation:

Area of triangle - Area of circle

Area of triangle = ½×14×14×sin(60)

= 84.87 cm²

Area of circle = pi × 4.04²

= 51.28 cm²

Shaded area = 84.87 - 51.28

= 33.6 cm²

1/2*qr*rs

step-by-step explanation:

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for