Question

A triangular plaque has side lengths of 8 inches, 13 inches, and 15 inches.

Use Heron's Formula to find the area of the plaque.

Answer 1

Answer: A) 52 square inches

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Step-by-step explanation:

a = 8, b = 13, and c = 15 are the sides of the triangle

s = (a+b+c)/2 = (8+13+15)/2 = 18 is the semi-perimeter, aka half the perimeter.

Those values are then plugged into Heron's Formula below

`A = √(s*(s-a)*(s-b)*(s-c))\\\\A = √(18*(18-8)*(18-13)*(18-15))\\\\A = √(18*(10)*(5)*(3))\\\\A = √(2700)\\\\A = √(900*3)\\\\A = √(900)*√(3)\\\\A = 30√(3)\\\\A \approx 51.9615\\\\A \approx 52\\\\`

The triangular plaque has an area of approximately 52 square inches.