Question

Find the area of a triangle having vertices at (-4,8); (3,-11); and (1,6)

Answer 1

check the picture below.

so, we can simply split that triangle, intwo two triangles, as you see in the picture, the blue and yellow ones.

notice, the blue one has a height of 2, a base of 5, whilst the yellow one has a base of 5 and a height of 17.

now, we can simply get the area area of each triangle, add them up, and that's the area of that larger triangle.

$\bf \stackrel{\textit{blue triangle's area}}{\cfrac{1}{2}(5)(2)}~~+~~\stackrel{\textit{yellow triangle's area}}{\cfrac{1}{2}(5)(17)}\implies 5+42.5\implies 47.5$