Question

Find the perimeter and area.
a.
(1,4), (4,5), (5,2)
b.
(0,–2), (0,2), (4,0)
c.
(0, 0), (2, 0), (4,–3)

Answer 1

for the perimeters, just find the lengths of the sides and add them up.

The areas are a bit trickier, but

(a) once you get the sides, you will see that it is a right triangle, so the area is easy.

(b) is easy, since it is easy to see that it is isosceles, with base=4 and height=4

(c) is a little tougher, but you can use Heron's formula, giving the area as
√(((7+√13)/2)((3+√13)/2)((-3+√13)/2)((7-√13)/2)) = 3

note that the line from (0,0) to (4,-3) is 3x+4y=0. The altitude is the distance from (2,0) to that line, which is 6/5, making the area = 3, or

note that the perpendicular to 3x+4y=0 through (2,0) is y = 4/3 (x-2). The two lines intersect at (32/25,-24/25), so the altitude is 6/5, making the area = 3

Answer 2

What tools do you have?
Do you know how to find the distance between two points?
Do you know how to find angles of a triangle knowing the sides?