Question

Triangle ABC, with vertices A(5,2), B(7,6), and C(2,5), is drawn inside a rectangle, as shown below.

Answer 1

9 units²

Explanation:

calculate the area of Δ ABC as

area of rectangle - area of 3 outer right triangles

area of rectangle = 5 × 4 = 20 units²

area of left Δ =
`(1)/(2)` × 3 × 3 = 4
`(1)/(2)` units²

area of Δ on right =
`(1)/(2)` × 2 × 4 = 4 units²

area of top Δ =
`(1)/(2)` × 5 × 1 = 2
`(1)/(2)` units²

Then

area of Δ ABC = 20 - 4
`(1)/(2)` - 4 - 2
`(1)/(2)` = 20 - 11 = 9 units²