You want to buy a triangular lot measuring 1370 feet by 1800 feet by 2480 feet. The price of the land is $2200 per acre.

Question

How much does the land cost? (Hint: 1 acre = 43,560 square feet. Round your answer to two decimal places.)

Answer 1

Calculate the perimeter.

p = (a+b+c)/2  = ( 1370+1800+2480)/2 =2825 ft

Calculate the area of the triangle using Heron's formula.

A =sqrt(p(p-a)(p-b)(p-c)) = sqrt(2825(2825-1370)(2825-1800)(2825-2480)) =1205624.88 ft^2

Covert the area from ft^2 to acres.

A = 1205624.88/43560 =27.68 acres

Calculate the cost of land.

Cost = (27.68)($2200) = $60,896