Question

Type the correct answer in each box. If necessary, round your answer(s) to the nearest hundredth. The vertices of ∆ABC are A(-2, 2), B(6, 2), and C(0, 8). The perimeter of ∆ABC is units, and its area is square units.

Answer 1

p=22.809

a=24

Explanation:

ahhhhh

Answer 2

`P=8+2√(10)+6√(2)\ units`

`A=24\ un^2.`

Explanation:

Plot the vertices of the triangle ABC on the coordinate plane and find the sides AB, BC and AC lengths:

`AB=√((-2-6)^2+(2-2)^2)=√((-8)^2+0^2)=√(64+0)=8\\ \\AC=√((-2-0)^2+(2-8)^2)=√((-2)^2+(-6)^2)=√(4+36)=2√(10)\\ \\BC=√((6-0)^2+(2-8)^2)=√(6^2+(-6)^2)=√(36+36)=6√(2)`

So, the perimeter of the triangle ABC is

`P=8+2√(10)+6√(2)\ units`

To find the area of the triangle, use the formula

`A=(1)/(2)\cdot \text{Base}\cdot \text{Height}`

In your case, AB is the base and the height is 6 units long (see attached diagram). Therefore,

`A=(1)/(2)\cdot 8\cdot 6=24\ un^2.`