A movable section of stage has the shape of an isosceles right triangle. You need to apply 2 coats of paint to all but the bottom. The paint covers approximately 90 square feet per quart. How many quarts of paint do you need to buy? You need to buy quarts of paint.
Answers
Answer:
You need to buy 3 quarts of paint.
Step-by-step explanation:
Given
[tex]Coats =2[/tex]
[tex]Paint = 90ft^2/qt[/tex]
See attachment for stage
Required
Determine the number of quarts needed
First, we calculate the surface area of the stage (without the base).
This is calculated as:
Area = Area of Rectangle1 + Area of Rectangle 2 + 2 * Area of each triangle on both sides.
For the first rectangle, we have:
[tex]A_1 =Length * Width[/tex]
[tex]A_1 = 15.2 * 19.5 =296.4[/tex]
For the second rectangle, we have:
[tex]A_2 =Length * Width[/tex]
[tex]A_2 = 6* 19.5 = 117[/tex]
For each triangle on both sides
[tex]A_3 = 0.5 * Base * Height[/tex]
[tex]A_3 = 0.5 * 14 * 6 = 42[/tex]
So, the total area is:
[tex]Area = A_1 + A_2 + 2 *A_3[/tex]
[tex]Area = 296.4 + 117+ 2 *42[/tex]
[tex]Area = 497.4ft^2[/tex]
The amount of paint need is:
[tex]Amount = \frac{Area}{2\ coats}[/tex]
From the question, we understand that:
[tex]1\ coat =90ft^2/quart[/tex]
Multiply both sides by 2
[tex]2 * 1\ coat =90ft^2/quart * 2[/tex]
[tex]2 \ coats =180ft^2/quart[/tex]
So, we have:
[tex]Amount = \frac{Area}{2\ coats}[/tex]
[tex]Amount = \frac{497.4ft^2}{180ft^2/quart}[/tex]
[tex]Amount = \frac{497.4ft^2}{180ft^2}quart[/tex]
[tex]Amount = \frac{497.4}{180}quart[/tex]
[tex]Amount = 2.763\ quarts[/tex]
[tex]Amount \approx 3\ quarts[/tex] --- approximated
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