Answer:[tex](5\pi-11.6)\ ft^{2}[/tex]Step-by-step explanation:we know thatThe area of the shaded region is equal to the area of the sector minus the area of the trianglestep 1Find the area of the circlethe area of the circle is equal to[tex]A=\pi r^{2}[/tex]we have[tex]r=5\ ft[/tex]substitute[tex]A=\pi (5)^{2}[/tex][tex]A=25\pi\ ft^{2}[/tex]step 2Find the area of the sectorwe know thatThe area of the circle subtends a central angle of 360 degreesso by proportion find out the area of a sector by a central angle of 72 degrees[tex]\frac{25\pi}{360}=\frac{x}{72}\\ \\x=72*25\pi /360\\ \\x=5\pi\ ft^{2}[/tex]step 3Find the area of triangleThe area of the triangle is equal to[tex]A=\frac{1}{2}(2.9+2.9)(4)= 11.6\ ft^{2}[/tex]step 4Find the area of the shaded regionSubtract the area of the triangle from the area of the sector[tex](5\pi-11.6)\ ft^{2}[/tex]