Triangle ABC has vertices as shown. What is the area of the triangle?
(1 point)
Responses
27–√
square units
2 square root of 7 square units
10.5 square units
10.5 square units
21 square units
21 square units
15−−√
square units
To find the area of the triangle, we can use the formula for the area of a triangle given its vertices:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
In this case, the vertices are A(3,1), B(7,4), and C(5,6).
Area = 1/2 * |3(4 - 6) + 7(6 - 1) + 5(1 - 4)|
Area = 1/2 * |3(-2) + 7(5) + 5(-3)|
Area = 1/2 * |-6 + 35 - 15|
Area = 1/2 * 14
Area = 7 square units
Therefore, the area of triangle ABC is 7 square units.