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

1 Answer
Alan P.
Oct 20, 2015

Area(triangle ABC) = 7Area(△ABC)=7

Explanation:

Geometric Solution
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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.

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