# The vertices of a triangle are the points with coordinates (3, 5), (9, 13), (10, 6). Prove that the triangle is isosceles. Calculate is area.

The three vertices are (3, 5), (9, 13), (10, 6)

Length of first side = √((9 - 3)2 + (13 - 5)2)

Length of first side = √(62 + 82)

Length of first side = 10 units

Length of second side = √((10 - 9)2 + (6 - 13)2)

Length of second side = √(12 + 72)

Length of second side = √50 units

Length of third side = √((10 - 3)2 + (6 - 5)2)

Length of third side = √(72 + 12)

Length of third side = √50 units

Since the length of second and third sides are equal so the triangle is isosceles

Length of height

Length of height = √75 units

Area = 0.5 × base × height

Area = 12.5 × 1.732

Area = 12.5 × 1.732 = 10.768 sq. units

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