Question

Using definite integral compute the area of the region bounded by the side of the triangle whose vertices are
(i) (2, 0),(4, 5) and (6, 3)
(ii) (-1, 1), (0, 5) and (3, 2)

Answer 1

(i) $(2,0),(4,5),(6,3)$

We can also caclulate Area like this

$\Delta =\frac{1}{2}\left|\begin{array}{ccc}2& 0& 1\\ 4& 5& 1\\ 6& 3& 1\end{array}\right|$

$=\frac{1}{2}\left(2\right(5-3)-4(-3)+6(-5\left)\right)$

$=\frac{1}{2}(4+12-30)$

$=\left|\frac{1}{2}\right(16-30\left)\right|$

$\left|\frac{1}{2}\right(14\left)\right|$

$=7$ square unit

(ii) $(-1,1),(0,5),(3,2)$

$\Delta =\frac{1}{2}\left|\begin{array}{ccc}-1& 1& 1\\ 0& 5& 1\\ 3& 2& 1\end{array}\right|$

$=\frac{1}{2}(-1(3)-0()+3(1-5\left)\right)$

$\frac{1}{2}(-3-12)=7.5$ sq.unit