Question

Compute the area in acres of a triangular parcel of land whose sides measure 45.66 mm, 84.1 mm, and 65.44 mm on a vertical photograph taken from 6040 ft above average ground with a 152.4 mm focal length camera.

Express your answer in ac. to four significant figures.

Answer 1

Solution -

Given Data

focal length (f) = 152.4 mm

Height of photograph (H) = 6040 ft

Length of line on photograph = x mm

Length of line on ground = X ft

Using the formula,

Scale = f / H = x/X

Putting values of sides, we can get the length of line on ground

a = 1809.622 ft

b = 3333.097 ft

c = 2593.554 ft

For finding the area of triangle with sides known, we will use heron's formula

s = (a+b+c)/2

Area = Sq. rt.[s * (s-a) * (s-b) * (s-c)]

Putting values, we will get

Area of triangle = 2330262.0331 ft² = 53.495455305326 acres

So, area of triangular parcel of land is 53.4955 acres.