Answer:
The area of the triangle is 7.5 unit²
Step-by-step explanation:
Here we have the coordinates given as
(-3, 5) (-3, 8) and (2, 5)
Let us call the points A = (-3, 5)
B = (-3, 8) and
C = (2, 5)
Therefore the lengths of the sides of the triangle are
AB = a = ![\sqrt{(-3-(-3))^2+(5-8)^2} = 3](https://tex.z-dn.net/?f=%5Csqrt%7B%28-3-%28-3%29%29%5E2%2B%285-8%29%5E2%7D%20%3D%20%203)
AC = b = ![\sqrt{(-3-2)^2+(5-5)^2} = 5](https://tex.z-dn.net/?f=%5Csqrt%7B%28-3-2%29%5E2%2B%285-5%29%5E2%7D%20%3D%20%205)
BC = c = ![\sqrt{(-3-2)^2+(8-5)^2} = \sqrt{34}](https://tex.z-dn.net/?f=%5Csqrt%7B%28-3-2%29%5E2%2B%288-5%29%5E2%7D%20%3D%20%20%5Csqrt%7B34%7D)
Therefore the Area can be derived from Heron's formula which is
A =
where s = semi perimeter or (a + b + c)/2
Therefore, plugging the values, we get
s = (3 + 5 + √34)/2 = 6.9155≈6.92
A =
= 7.499≈7.5.