Window area question, express as function of Area

In summary, the conversation discusses a window with the shape of a rectangle surmounted by an equilateral triangle. The perimeter of the window is given as 15 feet and the area is expressed as a function of one side of the equilateral triangle. The equations for the area of an equilateral triangle, surface area of the window, and volume of the window are provided. The suggested approach is to use the formula for the area of an equilateral triangle and the given perimeter to find the area of the window. A suggestion is also made to use MATLAB to create a function that takes the length of
  • #1
lovemake1
149
1

Homework Statement



A window has the shape of a rectangle surmounted by an equilateral triangle. Given that the perimeter of the window is 15 feet, express the area as a function of the length of one side of the equilateral triangle.

Homework Equations



Area of an equaliteral triangle : x^2(sqrt (3)) / 4

Surface area of the window : 3x + 2y = 15
reduced to : y = (15 - 3x) / 2

Volume of the window: X^2(sqrt(3)) / 4 + xy

The Attempt at a Solution



y = (15 - 3x) / 2 has domain of 0 <= x <= 5

i subbed in y into the vlume of the window,
x^2(sqrt(3)) / 4 + x(15-3x)/2

and after factoring out the x, I got [x(x*Sqrt(3) - 6x + 30)] / 4
and with new domain 0 < x < 5.


Am i takin the right approach? am i suppose to leave the sqrt where it is right now?
please help
 
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  • #2
Wouldn't the perimeter be 2x+2y=15? Then the area of the window is given by A=xy, but you know that x+y=7.5, then...
 
  • #3
hunt_mat said:
Wouldn't the perimeter be 2x+2y=15? Then the area of the window is given by A=xy, but you know that x+y=7.5, then...

No, you're missing the equilateral triangle.

Lovemake1 yes that's perfect.
 
  • #4
No, it says the perimeter of the 15, if the triangle fits snugly into the rectangle and the sides of the triangle is L, the one side is length L and the other side is given by [tex]L\sqrt{3}/2[/tex], so the area is given by [tex]L^{2}\sqrt{3}/2[/tex].
 
  • #5
Surmounted means to sit on top of, not to sit snugly into.

And by the way, for an equilateral triangle, if one side is length L then the area is [tex]\frac{\sqrt{3}}{4}L^2[/tex]
 
  • #6
Ah! I read surrounded.
 
  • #7
hunt_mat said:
Ah! I read surrounded.

That would make for a weird question :tongue:
 
  • #8
Not quite, it would mean that you could get a number for the area by using the perimeter.

Mat
 

1. What is the formula for calculating the window area as a function of total area?

The formula for calculating the window area as a function of total area is: window area = total area * window percentage.

2. How do you determine the window percentage?

The window percentage can be determined by dividing the window area by the total area and multiplying by 100.

3. Can the window area function be used for any shape or size of window?

Yes, the window area function can be used for any shape or size of window as long as the total area and window percentage are known.

4. Why is it important to express the window area as a function of the total area?

Expressing the window area as a function of the total area allows for easy comparison between different sizes and shapes of windows. It also allows for easier calculation of the window area for different total areas.

5. How can the window area function be used in building design and energy efficiency?

The window area function can be used in building design to optimize the amount of natural light and ventilation in a space. It can also be used to calculate the impact of windows on energy efficiency by determining the amount of heat gain or loss through the windows.

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