Question

Help me with this please!

Answer 1

Area = 20√2 is the area of triangle.

Explanation:

We have given the triangle in the graph.

We have to find the area of the triangle.

The formula for the area of triangle is :

Area = 1/2(base×height)

In the graph, the base is represented by AC, and height is represented

by AB.

First, we use distance formula to find AC and AB.

Base = AC =√(9-1)² + (-5-3)² = 8√2

Height = AB=√(4-1)² +(7-3)² = 5

Put this values of height and base in the formula we get,

Area = 1/2 (8√2 ×5)

Area = 20√2 is the area of triangle.

Answer 2

Area of triangle = 20√2

Explanation:

Formula:

Area of triangle = bh/2

b - base of triangle

h - height of triangle

Distance formula

d = √(x₂ - x₁)² +(y₂ - y₁)²

From the figure we can see that, the given triangle is right angled triangle.

Base = AC and Height = AB

To find AB and AC

A(1,3), B(4,7) and C(9, -5)

AB = √(4 - 1)² +(7 - 3)² = √(3² + 4²) = 5

AC = √(9 - 1)² +(-5 - 3)² = √(8² + -8²) = 8√2

To find the are of triangle

Area = bh/2 = (5* 8√2)/2 = 20√2

Therefore the area of triangle = 20√2 square units