Answer:
[tex]\displaystyle A=\frac{3h^2}{2}+h[/tex]
Step-by-step explanation:
Area of trapezoid
Given a trapezoid shape whose parallel sides measure b1 and b2 and whose height (perpendicular to the base) is h, then the area of the trapezoid is given by
[tex]\displaystyle A=\frac{b_1+b_2}{2}\cdot h[/tex]
The dulcimer has the following dimensions
[tex]b_1=2h+1[/tex]
[tex]b_2=h+1[/tex]
and height h
Thus
[tex]\displaystyle A=\frac{2h+1+h+1}{2}\cdot h=\frac{3h+2}{2}\cdot h[/tex]
Operating
[tex]\displaystyle A=\frac{3h^2+2h}{2}=\frac{3h^2}{2}+h[/tex]
[tex]\boxed{A=\frac{3h^2}{2}+h}[/tex]
Is the required polynomial
