Problem 924

A triangular lot is 160 ft on one side and has a property line of length 850 ft. Find the area if the lot in acres.






Use the Pythagorean theorem to find the length of the other side of the lot.

base2 +height2  = hypothenuse2

height = \sqrt{hypothenuse^{2}-base^{2}}


\approx 835 ft

Use the formula for the area of a triangle below.

A = \frac{1}{2}*base*height

A = \frac{1}{2}*160*835

= 66800 ft2

The last step is to convert the area from square feet to acres. Remember that 1 acre 1 acre is equal to  43560 square feet.

66800 ft2*\frac{1 acre}{43560ft^{2}}\approx1.53 acres

The area of the lot is about 1.53 acres.



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