Question

find the area of triangle abc with the given parts. round to the nearest square centimeter.
a = 19.5 cm
b = 14.5 cm
c = 14.9 cm

a. 113 cm²
b. 116 cm²
c. 110 cm²
d. 107 cm²

Explanation:

Step1: Calculate the semi - perimeter \(s\)

The formula for the semi - perimeter of a triangle is \(s=\frac{a + b + c}{2}\).
Substitute \(a = 19.5\), \(b = 14.5\), and \(c = 14.9\) into the formula:
\(s=\frac{19.5+14.5 + 14.9}{2}=\frac{48.9}{2}=24.45\)

Step2: Use Heron's formula to find the area \(A\)

Heron's formula is \(A=\sqrt{s(s - a)(s - b)(s - c)}\)
Substitute \(s = 24.45\), \(a = 19.5\), \(b = 14.5\), and \(c = 14.9\) into the formula:

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First, calculate \(24.45\times4.95 = 121.0275\), \(9.95\times9.55=95.0225\)
Then \(121.0275\times95.0225\approx11500\)
\(A=\sqrt{11500}\approx107.24\approx107\) (rounded to the nearest square centimeter)

Answer:

D. \(107\space cm^{2}\)