# What is the area of a triangle whose vertices are the points with coordinates (3,2) (5,10) and (8,4)?

##### 2 Answers

Refer to explanation

#### Explanation:

1st solution

We can use Heron formula which states

The area of a triangle with sides a,b,c is equal to

No using the formula to find the distance between two points

we can calculate the length of sides between the three points given

let say

After that, we substitute to Heron formula.

2nd Solution

We know that if

Area of the triangle

Therefore the area of the triangle whose vertices are

Area of the triangle

#### Explanation:

**Method 1: Geometric**

**Method 2: Herons Formula**

Using the Pythagorean Theorem we can calculate the lengths of the sides of

then we can use Heron's Formula for the area of a triangle given the lengths of its sides.

Because of the number of calculations involved (and the need to evaluate square roots), I did this in a spreadsheet:

Again (fortunately) I got an answer of