Question

The vertices of AABC are A(-2, 2), B(6, 2), and C(0, 8). The perimeter of AABC is __________ units, and its area is __________ square units

Answer 1

The perimeter of triangle ABC is 24 units and its area is 18 square units.

Step-by-step explanation:

To find the perimeter of triangle ABC, we need to calculate the length of each side and add them up. The distance between points A and B is 6 units, the distance between points B and C is 8 units, and the distance between points C and A is 10 units. So the perimeter is 6 + 8 + 10 = 24 units.

To find the area of triangle ABC, we can use the formula: Area = 1/2 * base * height. The base of the triangle is the distance between points A and B, which is 6 units. The height is the distance between point C and the line containing points A and B, which is the y-coordinate of point C minus the y-coordinate of the line containing points A and B. So the height is 8 - 2 = 6 units. Therefore, the area of triangle ABC is 1/2 * 6 * 6 = 18 square units.