Question

How do you find the area of a triangle whose vertices are (1,4) (-4,-5) and (2,3)?

Answer 1

`Area(triangle ABC) = 7`

Explanation:

Geometric Solution

`triangle ABC= triangle ABD + square BCED - triangle ACE`

`color(white)("XXXXX")= ((5xx9)/2) + ((8+9)/2xx1)- ((6xx8)/2)`

`color(white)("XXXXX")=22 1/2 + 8 1/2 - 24`

`color(white)("XXXXX")=7`

Alternative Method
Calculate the length of each side of `triangle ABC` using Pythagorean Theorem.

Use Heron's Formula (`sqrt(s(s-a)(s-b)(s-c))` ) to calculate the area.