Question

For a project, Carlos must provide one cut-out paper model of each type of triangle: acute, right, and obtuse. He sketches each triangle on graph paper before making the models.

On a coordinate plane, 3 triangles are shown. One triangle has points (3, 3), (3, 6), (6, 3). Another triangle has points (5, 7), (4, 10), (7, 8). Another triangle has points (7, 1), (7, 6), and (9, 4).

What is the total area of the three triangles?

12.5 square units
13 square units
13.5 square units
14 square units

Answer 1

Compute each triangle's area.

Triangle 1: (3,3),(3,6),(6,3). Legs of length 3 and 3 → area = 1/2·3·3 = 4.5.

Triangle 2: (5,7),(4,10),(7,8). Shoelace:
Area = 1/2|5·10 + 4·8 + 7·7 − (7·4 + 10·7 + 8·5)|
= 1/2|131 − 138| = 1/2·7 = 3.5.

Triangle 3: (7,1),(7,6),(9,4). Base = 5 (vertical), height = 2 → area = 1/2·5·2 = 5.

Total = 4.5 + 3.5 + 5 = 13 square units.

Answer: 13 square units.