you design the wooden poster frame and paint the front surface.

Question

write a polynomial that represents the area of wood you paint.

you design the frame to display a 16 inch by 20 inch poster. how much wood?

 

Answer 1

Well....a few unknowns in the problem description....Assuming the poster frame is rectangular.

and h represents the distance between the inner edge & the outer edge of the frame, and h remains constant around the entire poster frame, then:

using the formula for the area of a trapezoid, A=(h/2)(a+b), where a & b are parallel,  we can conclude the following:

if a=known inner frame length and b=unknown outer frame length,

Area of the top & bottom are each A₁=(h/2)(16+16+x) 

Area of the left & right are each A₂=(h/2)(20+20+y)

So total of the top & bottom areas=2A₁ = h(x+32)

and total of the left & right areas=2A₂ = h(y+40)

Adding the two areas together yields h(x+32)+h(y+40) = h(x+32+y+40) = h(x+y+72)  sq in

With x and y being equal to 2h, that makes the expression h(2h+2h+72)=4h^2+72h. I hope this helps....