A triangular parcel of land has sides of lengths 900, 580, and 550 feet. Approximate the area of the land. Round answer to nearest foot.
A) $154,345 \mathrm { ft } ^ { 2 }$
B) $153,657 \mathrm { ft } ^ { 2 }$
C) $152,972 \mathrm { ft } ^ { 2 }$
D) $152,971 \mathrm { ft } ^ { 2 }$
E) $153,656 \mathrm { ft } ^ { 2 }$

Question

A triangular parcel of land has sides of lengths 900, 580, and 550 feet. Approximate the area of the land. Round answer to nearest foot. 
A) $154,345 \mathrm { ft } ^ { 2 }$
B) $153,657 \mathrm { ft } ^ { 2 }$
C) $152,972 \mathrm { ft } ^ { 2 }$
D) $152,971 \mathrm { ft } ^ { 2 }$
E) $153,656 \mathrm { ft } ^ { 2 }$

Quizplus · Accepted Answer

To approximate the area of the triangular parcel of land, we can use Heron's formula, which is $A = \sqrt{s(s-a)(s-b)(s-c)}$, where $s$ is the semi-perimeter of the triangle and $a$, $b$, and $c$ are the lengths of the sides. First, calculate the semi-perimeter: $s = \frac{900 + 580 + 550}{2} = 1015$. Then, plug the values into Heron's formula: $A = \sqrt{1015(1015-900)(1015-580)(1015-550)}$, which gives an approximate area of $153,657 \mathrm { ft } ^ { 2 }$, rounded to the nearest foot.

A Triangular Parcel of Land Has Sides of Lengths 900 154,345ft2154,345 \mathrm { ft } ^ { 2 }154,345ft2

A Triangular Parcel of Land Has Sides of Lengths 900 $154,345 \mathrm { ft } ^ { 2 }$