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

Answer:

9 units²

Step-by-step 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 = $\frac{1}{2}$ × 3 × 3 = 4 $\frac{1}{2}$ units²

area of Δ on right = $\frac{1}{2}$ × 2 × 4 = 4 units²

area of top Δ = $\frac{1}{2}$ × 5 × 1 = 2$\frac{1}{2}$ units²

Then

area of Δ ABC = 20 - 4 $\frac{1}{2}$ - 4 - 2 $\frac{1}{2}$ = 20 - 11 = 9 units²