A Somewhat Large Cake

[studdo]

The aproach with the division of the quadrilateral into a parallelogram and a triangle makes most sense. Hats off!!!

[Gromy]

BRAHMAGUPTA was a 7th Century Hindu mathematician. He found a formula for the area of cyclic quadrilaterals.

The answer is just over 146 sq feet

[Legend of Tenshi]

Originally posted by lepton:

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Pretend it's flat or something

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Mmmm.... Lamina Cake

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I'm looking for a good sig, wanna help?

[Deathstream]

okay i'm guessing 148.5
I used a propety i made up and haven't tested and will never test unless by some miracle of a chance it's right.
Lepton u should make a program or something that will do this after.
If you make it for ti-83+ calcs that would b great.
when's the answer 4 this one and the marble one going up. I thik i got the marble one right but it probably won't be checked until tomorrow.
Lepton solve this one. "a" is irrational. "b" is irrational. a^b is rational. What is "a" and "b". If you've never done it before and can't get the answer then your no mathmatician.



[This message has been edited by Deathstream (edited 05-19-2004 11:45 PM).]

[kevinatilusa]

I don't think Brahmagupta's formula applies here...for the shape to be cyclic it would have to be opposite angles adding to 180, not adjacent ones.

[Marcus210]

This couldn't be cyclic. With two sides parallel the other two sides would have to be equal.

[dARKhORN]

The area of the cake is 109.137 ft sq with angels C=124.229, A=55.771, K=138.590, E=41.410, with C being the corner for the 8ft and 18ft sides.

[Deathstream]

it's smallest area possible is 120 because if u have an 8 by 15 cake it is 120 but in this cake the 2 of the sides are longer creating a larger area.

[This message has been edited by Deathstream (edited 05-22-2004 08:46 PM).]

[dimarxia]

Though that is true for rectangles, Deathstream, the dimensions and angle descriptions suggest a trapezoid. I worked it out and got the same answer as dARKhORN.

[Deathstream]

i was guessing that it was true with all shapes

[What if...]

I stopped not existing. Hi mikegoo!

[althedrum]

This is my first time on your site and I've been following the thread in some bewilderment. It seems to me that you are all trying to outthink this problem and I'm sorry, but I don't agree with the posted answer either. The top of the cake must be a trapezium with two parallel faces of 18 and 15 respectively, and two opposingly sloped faces of 10 and 8 respectively. Put two of these together by mirroring one to get a parallelogram of two sides 33 and two sides 8 and you get a surface area of 33 X 8 = 264. divide this by two to get the area of one shape = 132sq units

[marcus210]

althedrum, I agree that people tend to overthink some of these problems. With some puzzles that's the whole idea.
The parallelogram idea works but you applied the formula for the area of a rectangle. The side of lenght 8 is sloped. You need to determine the perpendicular distance between the parallel sides to get the area correct.

[althedrum]

it doesn't matter that the 8 side is sloped - in a parrallelogram opposite angles are equal, this means that, in effect, you can push the sloping sides to perpendicular to make all four angles 90 degrees - a parralellogram is just a rectangle that has been italicised. Put another way, you can cut one triangle off the end and add it to the other. either way you get a rectangle.

[Lucky Wizard]

althedrum: Your logic doesn't quite work, since the rectangle you get when you chop of the triangle and move it to the other end does not have a side of length 8; it has a side of a shorter length, since the side now connects the other pair of sides directly instead of being slanted, and the distance between two parallel lines is shorter if the line representing the distance is not slanted.