# Area in feet squared and inches squared

9. What is the area of a rectangular floor measuring 15 ft 3 in. by 12 ft 9 in.? (1 foot = 12 inches)

A) 162 ft^2 93 in^2

B) 178 ft^2 23 in^2

C) 194 ft^2 63 in^2

D) 180 ft^2 27 in^2

E) 192 ft^2 36 in^2

This question is from the Open Division of the 3^{rd} International Vedic Mathematics Olympiad held last Nov 25, 2023. The conventional solution would be to convert the measurements to inches, perform the multiplication and convert the answer to ft^2 and in^2.

Converting the measurements to inches can be done easily mentally: 15 ft 3 inches = 15(12) + 3 = 183 inches while 12 feet 9 inches = 12(12) + 9 = 149 inches. But the following computations will not be easy without using pen and paper: (183 x 149)/144.

Using the Vertically and Crosswise general multiplication method of Vedic Math however, this problem can be solved mentally:

15 ft + 3 in

12 ft + 9 in

180 ft^2 + 171 ft-in + 27 in^2

= 180 ft^2 + 168 ft- in + 3 ft-in + 27 in^2

= 180 ft^2 + 168/12 ft^2 + 3(12) in^2 + 27 in^2

= 194 ft^2 + 63 in^2

Now if we treat 15 ft and 3 inches as 15 1/4 feet and 12 ft and 9 inches as 12 3/4 feet and using the V&C method like the FOIL method of multiplying binomials, an easier solution is available.

(15 1/4) ft x (12 3/4 ft) = [15(12) + 15(3/4) + 1/4 (12) + (1/4)(3/4)] ft^2

= [180 + 45/4 + 3 + 3/16] ft^2

= 180 + 11 + 1/4 + 3 + 3/16] ft^2

= [194 + 7/16] ft^2

= 194 ft^2 63 in^2