Question

He vertices of ?ABC are A(2, 8), B(16, 2), and C(6, 2). The perimeter of ?ABC is units, and its area is square units.

Answer 1

Perimeter = 32.44 unit

Area of triangle = 30 unit²

Explanation:

By distance formula distance between (a,b) and (c,d) is
`√((c-a)^2+(d-b)^2)`

So, we have

`AB=√((16-2)^2+(2-8)^2)=15.23\\\\BC=√((16-6)^2+(2-2)^2)=10\\\\AC=√((2-6)^2+(8-2)^2)=7.21`

Perimeter = 15.23 + 10 + 7.21 = 32.44 unit

We have
`s=(15.23+10+7.21)/(2)=16.22`

Area of triangle
`=√(s(s-AB)(s-BC)(s-AC))=√(16.22(16.22-15.23)(16.22-10)(16.22-7.21))=30`

Area of triangle = 30 unit²