Question

a triangular lot is 130 ft on one side and has a property line of length 700 ft. Find the area of the lot in acres.

Answer 1

Answer:

Area of the lot = 1.03 acres

Explanations:

The line length of the triangular lot = 700 ft

The height of the triangular lot = 130 ft

Note:

Area of a triangle = 0.5 x base x height

Calculate the base of the triangular lot using the Pythagora's theorem

`\begin{gathered} \text{Length}^2=Height^2+Base^2 \\ 700^2=130^2+Base^2 \\ \text{Base}^2=700^2-130^2 \\ \text{Base}^2\text{ = }490000\text{ - }16900 \\ \text{Base}^2\text{ = }473100 \\ \text{Base = }\sqrt[]{473100} \\ \text{Base = }687.82 \end{gathered}`

The base of the triangular lot = 687.82 ft

Area of the triangular lot = 0.5 x 687.82 x 130

Area of the triangular lot = 44708.3 ft²

NB

1 ft² = 2.3 x 10^(-5) Acres

44708.3 ft² = 44708.3 x 2.3 x 10^(-5)

44708.3 ft² = 1.03 acres

Therefore:

Area of the lot = 1.03 acres