Answer:
a) 5.7 liters
b) 7.7 liters
Step-by-step explanation:
Part a
To determine how much varnish Ricardo will need to stain the hardwood floor his living room, given that 1 liter of finish covers 4.5 square meters, we need to divide the area of the floor by the coverage area of the varnish per liter.
The floor of Ricardo's living room is made up of a rectangle and a trapezoid.
The dimensions of the rectangle are:
[tex]\sf Width: w=2.2\; m\\\\Length: l = 7.5 \; m[/tex]
The bases (b₁ and b₂) of the trapezoid are:
[tex]\sf b_1 = 3.5\;m\\\\b_2 = 7.5\;m-2.0\;m=5.5\;m[/tex]
The height (h) of the trapezoid is:
[tex]\sf h = 4.2 \;m - 2.2\; m = 2.0\; m[/tex]
The area of the floor is the sum of the area of the rectangle and the trapezoid. Therefore:
[tex]\textsf{Area of floor}=\textsf{Area of rectangle}+\textsf{Area of trapezoid}\\\\\\\textsf{Area of floor}=w \times l+\dfrac{1}{2}(b_1+b_2)h\\\\\\\textsf{Area of floor}=2.2 \times 7.5+\dfrac{1}{2}(3.5+5.5)2.0\\\\\\\textsf{Area of floor}=16.5+9\\\\\\\textsf{Area of floor}=25.5\; \sf m^2[/tex]
Now, divide the area of the floor by the coverage area of the varnish per liter, which is 4.5 square meters:
[tex]\textsf{Amount of varnish needed}=\dfrac{25.5}{4.5}\\\\\\\textsf{Amount of varnish needed}=5.666...\\\\\\\textsf{Amount of varnish needed}=5.7\; \sf liters[/tex]
So, the amount of varnish Ricardo will need to stain the hardwood floor of his living room is:
[tex]\Large\boxed{\boxed{\sf 5.7\; liters}}[/tex]
[tex]\dotfill[/tex]
Part b
To determine how much paint Ricardo will need to paint the walls of his living room, given that 1 liter of paint covers 7.5 square meters, we need to divide the total area of the walls by the coverage area of the paint per liter.
To find the total area of the walls of the living room, multiply its perimeter by the height of the room, which is 2.6 meters.
[tex]\textsf{Total area of walls}=\textsf{Perimeter} \times 2.6\\\\\\\textsf{Total area of walls}=(3.5+2.8+2.0+2.2+7.5+4.2) \times 2.6\\\\\\\textsf{Total area of walls}=22.2 \times 2.6\\\\\\\textsf{Total area of walls}=57.72\; \sf m^2[/tex]
Now, divide the total area of the walls by the coverage area of the paint per liter, which is 7.5 square meters:
[tex]\textsf{Amount of paint needed}=\dfrac{57.72}{7.5}\\\\\\\textsf{Amount of paint needed}=7.696\\\\\\\textsf{Amount of paint needed}=7.7\; \sf liters[/tex]
So, the amount of paint Ricardo will need to pain the walls of his living room is:
[tex]\Large\boxed{\boxed{\sf 7.7\; liters}}[/tex]
