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# What is the number of square units in the area of a triangle

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What is the number of square units in the area of a triangle whose sides measure 5, 6 and 6 units?

Nov 19, 2020

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Acute isosceles triangle.

Sides: a = 6   b = 6   c = 5

Area: T = 13.636

Perimeter: p = 17

Semiperimeter: s = 8.5

Angle ∠ A =  65.376° = 65°22'32″ = 1.141 rad

Angle ∠ B =  65.376° = 65°22'32″ = 1.141 rad

Angle ∠ C =  49.249° = 49°14'55″ = 0.86 rad

The triangle's area using Heron's formula.

Heron's formula gives the area of a triangle when the length of all three sides are known. There is no need to calculate angles or other distances in the triangle first. Heron's formula works equally well in all cases and types of triangles.

T = sqrt{ s(s-a)(s-b)(s-c) },

T =sqrt{ 8.5(8.5-6)(8.5-6)(8.5-5) }

T =sqrt{ 185.94 } = 13.64 units^2

Nov 19, 2020
edited by Guest  Nov 19, 2020
#2
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What is the number of square units in the area of a triangle whose sides measure 5, 6, and 6 units?

Height    h = sqrt(62 - 2.52) = 5.454356057

Area      A = 2.5 * 5.454356057 = 13.63589014 units squared

Nov 19, 2020