Find the area of the following shapes: 1) 10 cm 9 cm 6 cm
1 answer:
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Just put the coefients in to a matrix
1x-6y-3z=4
-2x+0y-3z=-8
-2x+2y-3z=-14
![\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\-2&2&-3|-14\end{array}\right]](https://tex.z-dn.net/?f=%20%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-6%26-3%7C4%5C%5C-2%260%26-3%7C-8%5C%5C-2%262%26-3%7C-14%5Cend%7Barray%7D%5Cright%5D%20)
mulstiply 2nd row by -1 and add to 3rd
![\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\0&2&0|-6\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-6%26-3%7C4%5C%5C-2%260%26-3%7C-8%5C%5C0%262%260%7C-6%5Cend%7Barray%7D%5Cright%5D)
divde last row by 2
![\left[\begin{array}{ccc}1&-6&-3|4\\-2&0&-3|-8\\0&1&0|-3\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%26-6%26-3%7C4%5C%5C-2%260%26-3%7C-8%5C%5C0%261%260%7C-3%5Cend%7Barray%7D%5Cright%5D)
multiply 2rd row by 6 and add to top one
![\left[\begin{array}{ccc}1&0&-3|-14\\-2&0&-3|-8\\0&1&0|-3\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-3%7C-14%5C%5C-2%260%26-3%7C-8%5C%5C0%261%260%7C-3%5Cend%7Barray%7D%5Cright%5D)
multiply 1st row by -1 and add to 2nd
![\left[\begin{array}{ccc}1&0&-3|-14\\-3&0&0|6\\0&1&0|-3\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-3%7C-14%5C%5C-3%260%260%7C6%5C%5C0%261%260%7C-3%5Cend%7Barray%7D%5Cright%5D)
divide 2nd row by -3
![\left[\begin{array}{ccc}1&0&-3|-14\\1&0&0|-2\\0&1&0|-3\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%26-3%7C-14%5C%5C1%260%260%7C-2%5C%5C0%261%260%7C-3%5Cend%7Barray%7D%5Cright%5D)
mulstiply 2nd row by -1 and add to 1st row
![\left[\begin{array}{ccc}0&0&-3|-12\\1&0&0|-2\\0&1&0|-3\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%26-3%7C-12%5C%5C1%260%260%7C-2%5C%5C0%261%260%7C-3%5Cend%7Barray%7D%5Cright%5D)
divide 1st row by -3
![\left[\begin{array}{ccc}0&0&1|4\\1&0&0|-2\\0&1&0|-3\end{array}\right]](https://tex.z-dn.net/?f=%20%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D0%260%261%7C4%5C%5C1%260%260%7C-2%5C%5C0%261%260%7C-3%5Cend%7Barray%7D%5Cright%5D)
rerange
![\left[\begin{array}{ccc}1&0&0|-2\\0&1&0|-3\\0&0&1| 4\end{array}\right]](https://tex.z-dn.net/?f=%5Cleft%5B%5Cbegin%7Barray%7D%7Bccc%7D1%260%260%7C-2%5C%5C0%261%260%7C-3%5C%5C0%260%261%7C%204%5Cend%7Barray%7D%5Cright%5D)
x=-2
y=-3
z=4
(x,y,z)
(-2,-3,4)
B is answer
1x-6y-3z=4
-2x+0y-3z=-8
-2x+2y-3z=-14
mulstiply 2nd row by -1 and add to 3rd
divde last row by 2
multiply 2rd row by 6 and add to top one
multiply 1st row by -1 and add to 2nd
divide 2nd row by -3
mulstiply 2nd row by -1 and add to 1st row
divide 1st row by -3
rerange
x=-2
y=-3
z=4
(x,y,z)
(-2,-3,4)
B is answer
Hope you can see the picture and understand the drawings.
It can seem complex at first but you just have to think it through.
I use pythagoras' theorem to find the diagonal of the base square and then use that information along with the height with the aid of that ever so handy pythagoras' theorem to find the length of the slope.
It can seem complex at first but you just have to think it through.
I use pythagoras' theorem to find the diagonal of the base square and then use that information along with the height with the aid of that ever so handy pythagoras' theorem to find the length of the slope.