Answer:
Stain required to stain the ramp = 2 quarts
Step-by-step explanation:
Area of the wheelchair ramp to be stained = Surface area of the ramp - Area of the rectangular base
Surface area of the ramp = 2(area of the triangular base) + (perimeter of the base)(height)
Area of the triangular base = [tex]\frac{1}{2}(\text{Base})(\text{Height of the triangle})[/tex]
= [tex]\frac{1}{2}(25)(\frac{25}{12})[/tex]
= [tex]\frac{625}{24}[/tex] in²
Perimeter of the triangular base = [tex]25\frac{1}{12}+25+\frac{25}{12}[/tex]
= 25 + [tex]\frac{1}{12}[/tex] + 25 + [tex]\frac{25}{12}[/tex]
= 50 + [tex]\frac{26}{12}[/tex]
= 50 + [tex]2+\frac{2}{12}[/tex]
= [tex]52\frac{1}{6}[/tex] ft
Surface area of the ramp = [tex]\frac{625}{12}[/tex] + [tex](52\frac{2}{12})\times 5[/tex] - 25×5
= [tex]\frac{625}{12}+\frac{3130}{12}-125[/tex]
= [tex]\frac{3755}{12}-125[/tex]
= 187.92 square feet
Since, 100 square feet area is covered by the stain = 1 quart
Therefore, 187.92 square feet will be covered by the stain = [tex]\frac{187.92}{100}[/tex]
= 1.8792
≈ 2 quarts
