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.

Plzzzz help fast

Answer 1

The polynomial that represents the area to be finished on the dulcimer shown is
`A=(3)/(2)h^2+h`

Explanation:

Given:

The given figure is a trapezium with opposite parallel to each other.

The opposite parallel sides are given as:

`b_(1)=2h+1\\b_(2)=h+1`

The height of the trapezoid is,
`h=h`

Now, the area of a trapezium is given as:

`A=(1)/(2)(\textrm{Sum of parallel sides)}* (Height)\\A=(1)/(2)(b_(1)+b_(2))* h\\A=(h)/(2)(2h+1+h+1)\\A=(h)/(2)(2h+h +1+1)\\A=(h)/(2)(3h+2)\\A=(3h^2)/(2)+(2h)/(2)\\A=(3)/(2)h^2+h`

Therefore, the polynomial that represents the area to be finished on the dulcimer shown is
`A=(3)/(2)h^2+h`