Find the perimeter and the area of the triangle with the given vertices. Round to the nearest tenth.?

Question

A (2,1)
B (3,6)
C (6,1)

Answer 1

Points A and C are at the same y-coordinate, meaning they form the base, with point B above them. Trivially, you can see that segment AC has a length of 4, and point B sits 5 units above them, so the height is 5. The area of a triangle is 0.5*b*h, where b is base and h is height, and you have both values. For the perimeter, you need the lengths of legs AB and BC. You need to use the Pythagorean theorem. In a right triangle, the length of the hypotenuse c is related to the lengths of the legs a and c by the equation a^2 + b^2 = c^2, or c = sqrt(a^2 + b^2). Now, when you have two points, (x1, y1) and (x2, y2), you can treat the line between them as the hypotenuse where the legs have lengths x1 - x2 and y1 - y2, so that's how you can calculate the lenghts of those legs, and add them to the length of the base, 4, to get the perimeter.