The points A, B, and C have co-ordinates (-4, 2), (7, 4) and (-3,-1). What is the area of the triangle ABC?

1 Answer
Feb 5, 2018

#A_t = color(green)(35.85)# sq. units

Explanation:

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Given : Three point A (-4, 2), B (7,4), C (-3, -1)

To find the area of the triangle.

Let's first find the three sides a, b, c and s, the semi perimeter of the triangle.

#a = sqrt((x_B - x_C)^2 + (y_B - y_C)^2)#

#a = sqrt(-3-7)^2 + (-1-4)^2) = sqrt(10^2 + 5^2) ~~11.18#

Similarly,

#b = sqrt((-3 - (-3))^2 + (-1-2)^2) = sqrt(6^2 + 3^2) ~~ 6.71#

#c = sqrt((-4-7)^2 + (2-4)^2) = sqrt (11^2 + 2^2) ~~ 11.18#

It's an isosceles triangle with sides a & c equal.

We will use the formula #A_t = sqrt(s (s-a), (s-b) (s-c))# to find the area of the triangle.

Semi perimeter of the triangle

#s = (a + b + c) /2 = 11.18 + 6.71 + 11.18) / 2 = 14.54#

#A_t = sqrt(14.54 (14.54 - 11.18) (14.54 - 6.71) (14.54 - 11.18)) = color(green)(35.85)# sq. units