P(3,20)Q(6,2) and R(6,8) i plotted the points and got a right angle triangle but now i need help finding the area?

http://mathcentral.uregina.ca/QQ/database/QQ.09.98/tyler1.html

To find the area of a right-angled triangle, you can use either the lengths of its sides or the coordinates of its vertices. Since you have the coordinates of the vertices, we'll use that approach.

Given the coordinates of the vertices P(3, 20), Q(6, 2), and R(6, 8), we can calculate the lengths of the sides using the distance formula.

1. Calculate the length of side PQ:
The distance formula for two points (x1, y1) and (x2, y2) is:
distance = √((x2 - x1)² + (y2 - y1)²)

Applying this formula to points P(3, 20) and Q(6, 2):
distance PQ = √((6 - 3)² + (2 - 20)²)
= √(3² + (-18)²)
= √(9 + 324)
= √333

2. Calculate the length of side QR:
Using the same distance formula, this time for points Q(6, 2) and R(6, 8):
distance QR = √((6 - 6)² + (8 - 2)²)
= √(0² + 6²)
= √0 + 36
= √36
= 6

3. Calculate the length of side RP:
Again, using the distance formula for points R(6, 8) and P(3, 20):
distance RP = √((3 - 6)² + (20 - 8)²)
= √((-3)² + 12²)
= √(9 + 144)
= √153

Now that we have the lengths of all three sides (PQ, QR, and RP), we can use the formula to calculate the area of a right-angled triangle:

Area = PQ * QR / 2

Substituting the values we found:

Area = (√333 * 6) / 2
= (√333 * 6) / 2
= 3√37

The area of the right-angled triangle with vertices P(3, 20), Q(6, 2), and R(6, 8) is 3√37 square units.