Question

Let the floor of a hall is covered with identical tiles which are in shape of triangle. One of the triangle has the vertices at $(-3,2),$ $(-1,-1)$ and $(1,2).$ If the floor of the hall is completely covered by $110$ tiles, then the area of the floor (in sq.units) is

Answer 1

Given vertices of the triangle are $(-3,2),(-1,-1)$ and $(1,2)$

Now, the area of a triangular tile
$=\frac{1}{2}\left|\begin{array}{cc}{x}_1& y_1\\ x_2& y_2\\ x_3& y_3\\ x_1& y_1\end{array}\right|$

$=\frac{1}{2}\left|\begin{array}{cc}-3& 2\\ -1& -1\\ 1& 2\\ -3& 2\end{array}\right|$

$=\frac{1}{2}\left|\right(3+2)+(-2+1)+(2+6\left)\right|$
$=\frac{1}{2}|12|=6$ sq. units

$\therefore$ Total required area $=6\times 110=660$ sq. units