Question

The vertices of ΔABC are A(2,8), B(16,2), and C(16,2). The perimeter of ΔABC is _______________ units, and its area is _______________ square units.

Answer 1

To find the perimeter of a triangle, use the distance formula to calculate the distance between its vertices and then add them together. To find the area, use the shoelace formula.

Step-by-step explanation:

To find the perimeter of a triangle, we need to calculate the distance between its vertices. We can use the distance formula to do this. The distance between two points (x1, y1) and (x2, y2) is given by the formula: d = sqrt((x2-x1)^2 + (y2-y1)^2).

Using this formula, we can find the distance AB, BC, and AC. Then, we simply add these distances together to get the perimeter of the triangle.

To find the area of a triangle, we can use the shoelace formula. This formula states that the area of a triangle with vertices (x1, y1), (x2, y2), and (x3, y3) is given by the formula: area = 0.5 * |(x1*(y2-y3) + x2*(y3-y1) + x3*(y1-y2))|.

Using this formula, we can find the area of triangle ABC.