Question

Triangle ABC, with vertices A(3,3), B(9,5), and C(6,9), is drawn on the coordinategrid below.8..1236What is the area, in square units, of triangle ABC?

Answer 1

Lets consider the points A (3,3), B(9,5), C(6,9), D(9,3), E(9,9) and F(3,9)

The area of the triangle ABC is given by the area of the square ADEF subtracted by the area of the triangles ADB, BEC and CFA.

The ADEF square has sides with length 6. Therefore, it's area is 6^2 = 36 square units.

The area of any triangle with base b and height h is (b*h)/2

For ADB triangle, we have b = 6 and h = 2, which implies (b*h)/2 = 6 square units

For BEC triangle, we have b = 3 and h = 4, which implies (b*h)/2 = 6 square units

And for CFA triangle, we have b = 3 and h = 6, which implies (b*h)/2 = 9 square units

Therefore, the area of ABC triangle is 36 - 6 - 6 - 9 = 15 square units