100Pts fast plz A triangular pen is modeled by △ABC. The vertices of △ABC are A(0, 8), B(12, 3), and C(7, –9). What is the area of the pen?

Question

asked Mar 15, 2022 198k views

1 Answer

Kasim Rangwala · Answer 1 · 2022-03-20T18:16:10+0000

Answer:

The area of the triangle is 84.511 square units.

Explanation:

First step, we need to calculate lengths of line segments AB, BC and AC by Pythagorean Theorem:

AB:

$AB = \sqrt{(12-0)^(2)+(3-8)^(2)}$

AB = 13

BC:

$BC = \sqrt{(7-12)^(2)+(-9-3)^(2)}$

BC = 13

AC:

$AC = \sqrt{(7-0)^(2)+(-9-8)^(2)}$

$AC \approx 18.385$

Now, we can determine the area of the triangle (
) by Heron's formula:

$A = √(s\cdot (s-AB)\cdot (s-BC)\cdot (s-AC))$ (1)

s = (AB+BC+AC)/(2) (2)

Where
is the semiperimeter of the triangle.

If we know that
AB = 13 ,
BC = 13 and
$AC \approx 18.385$ , then the area of the triangle is:

s = 22.193

A = 84.511

The area of the triangle is 84.511 square units.