Question

Find the area of the triangle formed by the points (2, 3), (–1, 0) and (2, –4) by using Heron’s formula

Answer 1

Given :

Coordinates of triangle

(2, 3), (–1, 0) and (2, –4)

To Find :

Area of triangle using heron's formula

Solution :

•Given triangle has its coordinates as A (2, 3), B(–1, 0) and C(2, –4)

•Now , AB = √[(2+1)²+(3-0)²]= √(9+9)

AB = √18 = 3√2 units

AC = √[(2-2)² + (3+4)²] = √(0 + 49)

AC = √49 = 7 units

BC = √[(2+1)² + (-4-0)²] = √[(3)²+(-4)²]

BC = √(9+16) = √25 = 5 units

•Now S =( AB + BC + AC )/2

S = (3√2 + 7 + 5 )/2

S = 6 + 3/√2

•Using Heron's formula

Area = √[s(s-a)(s-b)(s-c)

Area =

√[(6+3/√2)(6-3/√2)(3/√2-1)(3/√2+1)]

Area = √[( 36 - 9/2)( 9/2 - 1 ) ]

Area = √[ ( 63/2 )( 7/2 ) ]

Area = √( 63×7 ) /4

Area = √441/4

Area = 21/2 sq units

Area = 10.5 sq units

•Hence , Area of given triangle is 21/2 sq. units or 10.5 sq. units