Question

the area of triangle formed by vertices (1,-1), (-4,a), (-3,-5) in 24sq. unit. find a

Answer 1

Area of the triangle is Δ=1/2[x1(y2−y3)+x2(y3−y1)+x3(y1−y2)]
The vertices are 
(1,-1), (-4,a), (-3,-5)
Given area =24 sq.units
substitute in above equation
consider
(x1,y1)=(1,-1)
(X2,y2)=(-4,a)
(X3,y3)=(-3,-5)

24= 1/2[1(a-(-5))+(-4)((-5)-(-1))+(-3)((-1)-(a))]
24= 1/2[ (a+5)+(-4)(-5+1)+(-3)(-1-a)]
24= 1/2 [a+5-4(-4)+3+3a]
24= 1/2[a+5+16+3+3a]
24=1/2[4a+8+16]
24=1/2[ 4a+24]
24×2=4a+24
48= 4a+24
48-24=4a
24=4a
a=24/4
a=6

I hope it will help you