Question

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.

Answer 1

`\displaystyle A=(3h^2)/(2)+h`

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

`\displaystyle A=(b_1+b_2)/(2)\cdot h`

The dulcimer has the following dimensions

`b_1=2h+1`

`b_2=h+1`

and height h

Thus

`\displaystyle A=(2h+1+h+1)/(2)\cdot h=(3h+2)/(2)\cdot h`

Operating

`\displaystyle A=(3h^2+2h)/(2)=(3h^2)/(2)+h`

`\boxed{A=(3h^2)/(2)+h}`

Is the required polynomial