find the area of triangle formed by the points (8,-5),(-2,-7)and (5,1) by using herons formula
Answers
To calculate the area of the triangle whose vertices are (0,16),(0,5) and(8,2).
We know that if (x,y1), (x2,y2) and (x3,y3) are the vertices of the triangle, then the area of the triangle is given by:
Area of the triangle = (1/2) |{(x2-x1)(y2+y1) +(x3-x2)(y3+y1)+(x1-x3)(y1+y2)}|
Therefore the area of the triangle whose vertices are (0,16), (0,5), (8 ,2) is given by:
Area of the triangle = (1/2) {(0-0)(16+5) +(8-0)((2+5) +(0-8)(2+16)}
Area of triangle = (1/2) |{0 + 56 - 144}|
Area of the given triangle = (1/2) * 88 = 44 sq units.
W can calculate the area by Heron's formula also:
Area of the triangle = sqrt{s(s-a)(s-b)(s-c)}, a, b ,c are sides of triangle, s = (a+b+c)/2.
a = sqrt(0+(16-5)^2 )= 11
b = sqrt[8^2+ (2-14)^2] = sqrt260 = 16.125..
c =sqrt[(8-0)*2+(2-5)^2] = sqrt73 = 8.544..
Therefore s = (11+sqrt260+sqrt73)/2 = 17.834..
Area of the triangle = sqrt{(17.834..)(6.834...)(1.7097..)(9.2902...)}
Area of the triangle = sqrt1935.999998
Area of the triangle = 43.999...sq units
Answer:
Step-by-step explanation:
Find the area of triangle formed by the points by using heron's formula
