Question

A triangle parcel of land has sides measuring 680 feet, 320 feet and 802 feet. If the land is alued ad $2100 per acre, what is the value of the land?

Answer 1

Explanation:

You can get an approximate answer for the area if you treat the triangle as isosceles (820≈827), with base b=110 feet and height h=820 feet. In that case,

A = (1/2) b*h = (1/2) 110*820 = 45100 ft2.

You get the exact answer from Heron's formula,

A = sqrt( s*(s-a)*(s-b)*(s-c) )

where s is half the perimeter, s = (820+827+110)/2 = 878.5 ft, so that

A = sqrt( 878.5*(878.5-820)(878.5-827)*(878.5-110) ) = 45099 ft² = 1.035 acre,

for a value of 2300*1.035=2381.