I need help with this problem. Given: BC = 10 inches AC = √50 inches m∠CBD = 60° m∠CAD = 90° Calculate the exact area of the shaded region. Show all work for full credit. picture shown!

Area of the shaded region = 23.33 in²

Step-by-step explanation:

Area of a sector =

Where θ = Central angle subtended by an arc

r = radius of the circle

Area of the sector BCD =

                                       = 52.36 in²

Area of equilateral triangle BCD =

                                                      =

                                                      = in²

                                                      = 43.30 in²

Area of the shaded portion in ΔBCD = 52.36 - 43.3

                                                             = 9.06 in²

Area of sector CAD =

                                 = 39.27 in²

Area of right triangle CAD =

                                            =

                                            =

                                            = 25 in²

Area of the shaded part in the ΔACD = 39.27 - 25

                                                                         = 14.27 in²

Area of the shaded part of the figure = 9.06 + 14.27

                                                                = 23.33 in²

$53.50

step-by-step explanation:

you have to subtract the amount of money chuck earned ($72.50) by the cost of the gas for the mower ($11.25) and the new string for the trimmer he bought ($7.75).

72.50-11.25=61.25

and then subtract $61.25 by the second thing he bought (the new string for the trimmer)

61.25-7.75=53.5

so in total it's $53.50 (53 dollars and 50 cents)