Question

What is the area of a triangle whose vertices are R(3, 4), S(6, 2), and T(7, 10)?
Enter your answer in the box.

Answer 1

According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.

How to calculate the area of a triangle by knowing its sides

In this question we must determine the lengths of the three sides of the triangle by Pythagorean theorem and then the area is determined by Heron's formula.

First, we determine the length of each side:

$RS = \sqrt{(6-3)^{2}+(2-4)^{2}}$

$RS = \sqrt{3^{2}+(-2)^{2}}$

$RS = \sqrt{13}$

$ST = \sqrt{(7-6)^{2}+(10-2)^{2}}$

$ST = \sqrt{1^{2}+8^{2}}$

$ST = \sqrt{65}$

$RT = \sqrt{(7-3)^{2}+(10-4)^{2}}$

$RT = \sqrt{4^{2}+6^{2}}$

$RT = \sqrt{80}$

Now we calculate the area of the triangle by Heron's formula:

$s = \frac{\sqrt{13}+\sqrt{65}+ \sqrt{80}}{2}$

s ≈ 10.306

$A = \sqrt{10.306 \cdot (10.306 - \sqrt{13})\cdot (10.306 - \sqrt{65})\cdot (10.306 - \sqrt{80})}$

A ≈ 14.525

According to Heron's formula, the area of a triangle whose vertices are R(x, y) = (3, 4), S(x, y) = (6, 2) and T(x, y) = (7, 10) has a value of approximately 14.525 units.

To learn more on triangles: https://brainly.com/question/2773823

#SPJ1

Answer 2

Answer:

14.525 units

hope this helps :)