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What's the total area of this triangle minus the rectangle?
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(LEG1*LEG2)/2 = area of a right triangle (this is a right triangle since we know that 2 angles are 45 degrees due to the opposite sides being equal.
So you do
((11*11)/2) - (2ft 5in* 3ft 2in) = total area of this triangle minus the rectangle
So you do
((11*11)/2) - (2ft 5in* 3ft 2in) = total area of this triangle minus the rectangle
Tenacious-V
Thinks his PR is better than yours.
it's an isosceles triangle, where 2 sides are equal. A right angle triangle is where 1 side is 90*.
Oh wait, now I remember.
You have to split it into two right triangles, a base of (15.5/2).
Use pythagorean theorem for the height....then it is (b*h)/2 for the area of each triangle. And those two areas together for the area of the isoceles triangle, then subtract the area of the rectangle.
Convert everything into inches first. They are obviously trying to fuck with you by giving you one measurement as 15.5 feet, but the others are in ft + inches.
You have to split it into two right triangles, a base of (15.5/2).
Use pythagorean theorem for the height....then it is (b*h)/2 for the area of each triangle. And those two areas together for the area of the isoceles triangle, then subtract the area of the rectangle.
Convert everything into inches first. They are obviously trying to fuck with you by giving you one measurement as 15.5 feet, but the others are in ft + inches.
ok, fine. say it's not a right triangle
You cut the triangle in half right down the middle.
A = 1/2 (15.5) = 7.75 ft
B = X
C = 11
A^2 + B^2 = C^2
(7.75)^2 + X^2 = 11^2
60.0625 + X^2 = 121
X^2 = 121 - 60.0625
X^2 = 60.9375
X = 7.8062474979979977573086164011747 <---yeah, you should probably do with with fractions, but I'm lazy.
X = 7.8062474979979977573086164011747 = B
Now that you know B, you take A * B, and then figure out the area of the rectangle, and substitute.
So tired.
You cut the triangle in half right down the middle.
A = 1/2 (15.5) = 7.75 ft
B = X
C = 11
A^2 + B^2 = C^2
(7.75)^2 + X^2 = 11^2
60.0625 + X^2 = 121
X^2 = 121 - 60.0625
X^2 = 60.9375
X = 7.8062474979979977573086164011747 <---yeah, you should probably do with with fractions, but I'm lazy.
X = 7.8062474979979977573086164011747 = B
Now that you know B, you take A * B, and then figure out the area of the rectangle, and substitute.
So tired.
Split the triangle right down the middle to get two right triangles. Use the pythagorean theorem to find the height to be about 7.8 feet. Then area equals 7.8*7.75 divided by 2. You have two equal triangles though so you can ignore the divide by 2 part. So area of triangle is about 61 and just minus the area of the rectangle after that. You should get an answer of around 52.8.
split triangle into two equal halfs by drawing a straight line down from the upper corner in the triangle.
focus on the left triangle that you have created.
cos alpha = 7.75/11 => alpha = 45.2 degrees
the line you created is sin 45.2 * 11 = 7.81 ft
area of triangle 7.81*7.75 = 60.5 ft
focus on the left triangle that you have created.
cos alpha = 7.75/11 => alpha = 45.2 degrees
the line you created is sin 45.2 * 11 = 7.81 ft
area of triangle 7.81*7.75 = 60.5 ft
Couldn't you just divide this into two right triangles by splitting the base in half, using the pythagorean theorem to find the new vertical side, using 1/2(base)*(height) to find the area of each right triangle and adding these two areas, then subtracting the area of the rectangle?
So it would be (converting all values to inches):
(132^2) - ((1/2(186))^2 = vertical^2
8775 = vert^2
vert = 93.67 inches
So now the area of each "half" right triangle that comprise the larger triangle would be:
1/2(93)*(93.67) = 4355.66 inches
Multiplying by two gives you the area of the total triangle, which would be 8711.31 inches. The area of the rectangle is just L*W, so it's 29*38 = 1102 inches. Subtracting 1102 inches from 8711.31 inches gives 7609.31 inches as the total area of the triangle minus that of the rectangle. Dividing this by 12^2 (inches) yields 52.84 sq. ft.
I hope this is correct, since it's been about 9-10 years since I've worked with triangles, longer for proofs.
Egg on my face if this is wrong.
So it would be (converting all values to inches):
(132^2) - ((1/2(186))^2 = vertical^2
8775 = vert^2
vert = 93.67 inches
So now the area of each "half" right triangle that comprise the larger triangle would be:
1/2(93)*(93.67) = 4355.66 inches
Multiplying by two gives you the area of the total triangle, which would be 8711.31 inches. The area of the rectangle is just L*W, so it's 29*38 = 1102 inches. Subtracting 1102 inches from 8711.31 inches gives 7609.31 inches as the total area of the triangle minus that of the rectangle. Dividing this by 12^2 (inches) yields 52.84 sq. ft.
I hope this is correct, since it's been about 9-10 years since I've worked with triangles, longer for proofs.
Egg on my face if this is wrong.
since two sides are equal, it's an isosceles triangle. and when you drop a perpendicular from the vertex of said triangle, it bisects the base. you know the length of the base.
so drop a perpendicular from the vertex, now you know what the base of the newly formed right triangle is. you also know the length of it's hypotenuse (11ft). so now you can find the height of this triangle using the pythagorean formula/identity. once you know the height, you can derive the area by using the formula for the area of a triangle (.5*base*height). multiply this area by two to get the area of the original triangle, and finally subtract the area of the rectangle (L*W) from it.
only thing trivial is to convert everything into either inches or feet and knowing the eucledean law of a perpendicular bisector (which sorta becomes intuitive from practice and common sense perhaps).
so drop a perpendicular from the vertex, now you know what the base of the newly formed right triangle is. you also know the length of it's hypotenuse (11ft). so now you can find the height of this triangle using the pythagorean formula/identity. once you know the height, you can derive the area by using the formula for the area of a triangle (.5*base*height). multiply this area by two to get the area of the original triangle, and finally subtract the area of the rectangle (L*W) from it.
only thing trivial is to convert everything into either inches or feet and knowing the eucledean law of a perpendicular bisector (which sorta becomes intuitive from practice and common sense perhaps).
nitewulf said:
That's exactly what I did, yet I still have this sneaking suspicion that people are calling me "sad" and other such hurtful things because I forgot to ultimately divide the answer by 144 (12^2, to get the answer in feet), and instead divided by 12 (forgetting that you have to square it). Never mind that I was typing very quickly and watching the game at the same time. I'm quite torn up over it.
Loki: the laughing stock of the forum.
(This has been my first and only "pity me" post; we now return you to your regularly scheduled programming
)Yikes. Just to sum up for those who are fumbling for answers:
1) Base times height, then divided by two, is the formula for all triangles.
1a) For a right triangle, this means leg 1 times leg 2.
2) The isosceles triangle above can be bisected and made into two right triangles.
3) The length of the second leg, which is also the height of the triangle, can then be found using the Pythagorean Theorem (which can only be used for right triangles). This is: a squared + b squared = c squared, where a and b are legs, and c is the hypotenuse (long leg). Substitute and solve for b. This should give you a figure of 60.0625 feet.
From there, it's gravy.
1) Base times height, then divided by two, is the formula for all triangles.
1a) For a right triangle, this means leg 1 times leg 2.
2) The isosceles triangle above can be bisected and made into two right triangles.
3) The length of the second leg, which is also the height of the triangle, can then be found using the Pythagorean Theorem (which can only be used for right triangles). This is: a squared + b squared = c squared, where a and b are legs, and c is the hypotenuse (long leg). Substitute and solve for b. This should give you a figure of 60.0625 feet.
From there, it's gravy.
well, even in square inches form the answer would be correct, there is no particular reasons to convert it into square feet or vice versa, unless specified otherwise.Loki said:That's exactly what I did, yet I still have this sneaking suspicion that people are calling me "sad" and other such hurtful things because I forgot to ultimately divide the answer by 144 (12^2, to get the answer in feet), and instead divided by 12 (forgetting that you have to square it). Never mind that I was typing very quickly and watching the game at the same time. I'm quite torn up over it.
Tenacious-V
Thinks his PR is better than yours.
Archaix said:
lol woops, my bad.... You know I meant 1 angle, not side....
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