Question

The vertices of a triangle are (-1,3) (6,3) and (-1,-4)

Find the area of the triangle
Please show all workings

Answer 1

24.5

Explanation:

To find the area with the coordinates provided:

(-1,3), (6,3), (-1,-4)

First we count the units that are inside the triangle which is area.

`(49)/(2)`

So we know that there are
`(49)/(2)` units and then we divide 49 by 2 which gets you 24.5.

49 ÷ 2 = 24.5

The answer is 24.5 units.

Answer 2

24.5 unit²

Explanation:

Area of ∆

= ½ | x₁(y₂ - y₃) + x₂(y₃ - y₁) + x₃(y₁ - y₂) |

= ½ | (-1)(3 -(-4)) + 6(-4 -3) + (-1)(3 - 3) |

= ½ | -7 - 42 |

= ½ | - 49 |

= ½ (49)

= 24.5 unit²

Method 2:

Let the vertices are A, B and C. Using distance formula:

AB = √(-1-6)² + (3-3)² = 7

BC = √(-6-1)² + (-4-3)² = 7√2

AC = √(-1-(-1))² + (4-(-3))² = 7

Semi-perimeter = (7+7+7√2)/2

= (14+7√2)/2

Using herons formula:

Area = √s(s - a)(s - b)(s - c)

here,

s = semi-perimeter = (14 + 7√2)/2

s - a = S - AB = (14+7√2)/2 - 7 = (7 + √2)/2

s - b = (14+7√2)/2 - 7√2 = (14 - 7√2)/2

s - c = (14+7√2)/2 - 7 = (7 + √2)/2

Hence, on solving for area using herons formula, area = 49/2 = 24.5 unit²