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Luda [366]
3 years ago
6

A craftsman is making a dulcimer with the same dimensions as the one shown. The surface shown requires a special, more durable t

ype of finish. Write a polynomial that represents the area to be finished on the dulcimer shown.

Mathematics
1 answer:
Bogdan [553]3 years ago
8 0

Answer:

\displaystyle A=\frac{3h^2}{2}+h

Step-by-step explanation:

<u>Area of trapezoid</u>

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=\frac{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=\frac{2h+1+h+1}{2}\cdot h=\frac{3h+2}{2}\cdot h

Operating

\displaystyle A=\frac{3h^2+2h}{2}=\frac{3h^2}{2}+h

\boxed{A=\frac{3h^2}{2}+h}

Is the required polynomial

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