Calculate the area of triangle at points A(1,8),B(4,7) and C(5/2),(15/2)?

To calculate the area of a triangle with coordinates of its vertices given, we can use the formula for the area of a triangle using the coordinates of its vertices:

Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|

Given points A(1,8), B(4,7), and C(5/2, 15/2), we can substitute the coordinates into the formula:

Area = 1/2 * |1(7 - 15/2) + 4(15/2 - 8) + 5/2(8 - 7)|

Area = 1/2 * |1(1/2) + 4(1/2) + 5/2|

Area = 1/2 * |1/2 + 2 + 5/2|

Area = 1/2 * |1/2 + 4/2 + 5/2|

Area = 1/2 * |10/2|

Area = 1/2 * 5

Area = 5/2

Therefore, the area of the triangle with vertices A(1,8), B(4,7), and C(5/2, 15/2) is 5/2 square units.

The area of the triangle with vertices (x1, y1), (x2, y2) and (x3, y3) is given by:
Area = 1/2 | (x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)) |

Using this formula, we can calculate the area of the triangle with vertices A(1,8), B(4,7) and C(5/2,15/2) as follows:
Area = 1/2 | (1(7 - 15/2) + 4(15/2 - 8) + 5/2(8 - 7)) |
= 1/2 | (1(-1/2) + 4(1/2) + 5/2(1)) |
= 1/2 | (-1/2 + 2 + 5/2) |
= 1/2 | (11/2) |
= 11/4

Therefore, the area of the triangle ABC is 11/4 square units.