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

Refer to explanation

first remedy

We can use Heron formula which states

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

After that, we substitute to Heron formula.

2nd Solution

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Method 1: Geometric

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To find the area of the triangle formed by the given vertices, you can use the formula for the area of a triangle given its coordinates.

Let's label the vertices A(3,2), B(5,10), and C(8,4).

Then, you can use the formula:

Area = |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2))/2|

Substitute the coordinates of the vertices into the formula:

Area = |(3(10-4) + 5(4-2) + 8(2-10))/2|

Calculate the expression:

Area = |(3(6) + 5(2) + 8(-8))/2|

Area = |(18 + 10 - 64)/2|

Area = |(-36)/2|

Area = |-18|

So, the area of the triangle formed by the given vertices is 18 square units.

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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