I need help with figuring out real estate measurements.?

Question

Can someone tell me how many acres this property would be....beginning at corner thence in a northerly direction for a distance of 370 feet,to a steel post:thence east for a distance of app. 1066 feet to a steel post:thence south for a distance of 280 feet to a post :thence in a westerly direction for a distance of 1050 feet in a westerly direction to the steel post at the point of beginning .How many acres would that be????

Answer 1

From the statement of directions you know that there is a 90° angle between the 1066 ft. side and the 280 ft. side.  This gives two triangles with a common side of 1,102.15970 ft.  The right triangle has an area

A = (1/2)(280)(1,066) = 149,240 ft^2

You can use Hero's formula on the 2nd triangle:

s = (1/2)(a + b + c)

A = √[s(s - a)(s - b)(s - c)]

s = (1/2)(370 + 1,050 + 1,102.15970)

s ≈ 1,261.07985

A ≈ √[(1,261.07985(1,261.07985 - 370)(1,261.07985 - 1,050)(1,261.07985 - 1,102.15970)]

A ≈ √[(1,261.07985(891.07985)(211.07985)(158...

A ≈ √37,695,104,563.076

A ≈ 194,152.3 ft^2

The total area, then, is

A ≈ 194,152.3 ft^2 + 149,240 ft^2

A ≈ 343,392.3 ft^2

Converting to acres,

A ≈ (343,392.3 ft^2)(1 acre/43,560 ft^2)

A ≈ 7.8832 acres ≈ 7.88 acres