Answer to Question #155516 in Civil and Environmental Engineering for gwen

Question

A rectangular lot was measured using a 50 m metallic tape which was 1.02 cm too short. The recorded distances were 170.55 m long by 137.05 m wide. What is the error in area introduced due to the erroneous length of tape?

Answer 1

Solution

The error in length is 1.02/(100×50) = 0.000204, so a meter of tape is 1.000204 meters in reality. That makes the true length of the lot 170.55×1.000204 m = 170.585 m, and the width 137.078 m.

The true area was 170.585×137.078 m² and the measured area 170.55×137.05 m².

That’s a true area of 23383 m² and a measured area of 23374 m².

The error in area is therefore 23383m² - 23374m² = 9m²