Question

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?

Answer 1

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 (
`A`) by Heron's formula:

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

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

Where
`s` 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.