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luda_lava [24]
1 year ago
7

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

Mathematics
1 answer:
natka813 [3]1 year ago
8 0

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

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