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.

Solution:-

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

base² +height² = hypothenuse²

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

= $\sqrt{850^{2}-160^{2}}$

$\approx 835 ft$

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.