Question

find the area of triangle abc with the given parts. round to the nearest square foot.
a = 46 ft
b = 52 ft
c = 64 ft

a. 1,478 ft²
b. 1,182 ft²
c. 1,773 ft²
d. 131 ft²

Explanation:

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

The formula for the semi - perimeter of a triangle is \(s=\frac{a + b + c}{2}\).
Given \(a = 46\) ft, \(b = 52\) ft, \(c = 64\) ft.
\(s=\frac{46+52 + 64}{2}=\frac{162}{2}=81\) ft.

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

Heron's formula is \(A=\sqrt{s(s - a)(s - b)(s - c)}\).
Substitute \(s = 81\), \(a = 46\), \(b = 52\), \(c = 64\) into the formula:
\(A=\sqrt{81(81 - 46)(81 - 52)(81 - 64)}\)
\(=\sqrt{81\times35\times29\times17}\)
\(=\sqrt{81}\times\sqrt{35\times29\times17}\)
\(=9\times\sqrt{17005}\)
\(\approx9\times130.4\)
\(=1173.6\approx1182\) \(ft^{2}\)

Answer:

B. \(1,182\ ft^{2}\)