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.​ (Figure not drawn to​ scale)

​(Round to the nearest hundredth as​ needed.)

Answer 1

Area of the lot = 1.03 acres

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 Pythagoras's theorem

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

Explanation:

Answer 2

Area of the lot = 1.03 acres

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 Pythagoras's theorem

`\text{Length}^2=\text{Height}^2+\text{Base}^2`

`700^2=130^2+\text{Base}^2`

`\text{Base}^2=700^2-130^2`

`\text{Base}^2=490000-16900`

`\text{Base}^2=473100`

`\text{Base}=√(473100)`

`\text{Base}=687.82`

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