Question

Find the area of the given triangle using the following formula:

Answer 1

Area of the triangle is 31

Explanation:

Looking at the figure, we get

a = 3

b = 4

c = -2

d = 7

e = -1

f = -6

Now the formula to calculate the are of triangle is:

`A=(1)/(2)\left|\begin{array}{ccc}a&b&1\\c&d&1\\e&f&1\end{array}\right|`

Now, putting values of a, b,c,d,e and f and finding determinant first

`A=(1)/(2)\left|\begin{array}{ccc}3&4&1\\-2&7&1\\-1&-6&1\end{array}\right| \\A=(1)/(2).3\left|\begin{array}{cc}7&1\\-6&1\end{array}\right| (-4) \left|\begin{array}{cc}-2&1\\-1&1\end{array}\right|1\left|\begin{array}{cc}-2&7\\-1&-6\end{array}\right|\\A=(1)/(2).3(7*1 -(1*-6)) (-4)(-2*1 -(1*-1)) 1(-2*-6 -(7*-1))\\A=(1)/(2).3(7+6)-4( -2+1)1(+12+7)\\A=(1)/(2).3(13)-4( -1)1(19)\\A=(1)/(2).(39+4+19)\\A=(1)/(2).(62)\\A=31`

So, area of the triangle is 31