A craftsman is making a dulcimer with the same dimensions as the one shown. The surface shown requires a special, more durable type of finish. Write a polynomial that represents the area to be finished on the dulcimer shown.Plzzzz help fast

Answer:The polynomial that represents the area to be finished on the dulcimer shown is [tex]A=\frac{3}{2}h^2+h[/tex]Step-by-step explanation:Given:The given figure is a trapezium with opposite parallel to each other.The opposite parallel sides are given as:[tex]b_{1}=2h+1\\b_{2}=h+1[/tex]The height of the trapezoid is, [tex]h=h[/tex]Now, the area of a trapezium is given as:[tex]A=\frac{1}{2}(\textrm{Sum of parallel sides)}\times (Height)\\A=\frac{1}{2}(b_{1}+b_{2})\times h\\A=\frac{h}{2}(2h+1+h+1)\\A=\frac{h}{2}(2h+h +1+1)\\A=\frac{h}{2}(3h+2)\\A=\frac{3h^2}{2}+\frac{2h}{2}\\A=\frac{3}{2}h^2+h[/tex]Therefore, the polynomial that represents the area to be finished on the dulcimer shown is [tex]A=\frac{3}{2}h^2+h[/tex]