Answer
$A_{total}=71.1~acres$
Work Step by Step
The total area of the lot is the sum of the areas of lots A, B and C.
To find the area of lot A, we use Heron's formula:
Where
$a=1400ft$
$b=1400ft$
$c=1800ft$
$s=\frac{1}{2}$$(1400ft+1400ft+1800ft)$
$s=2300ft$
and
$A=\sqrt {s(s-a)(s-b)(s-c)}$
So,
$A=\sqrt {2300ft(2300ft-1400ft)(2300ft-1400ft)(2300ft-1800ft)}$
$A=965,142ft^{2}$
To find the area of lot B, use the formula for the area of a rectangle, $A=bh$.
Where
$b=1800ft$
$h=1000ft$
So, we have:
$A=bh=(1800ft)(1000ft)=1,800,000ft^{2}$
To find the area of lot C, we calculate the area of the right triangle using the formula: $A=\frac{bh}{2}$.
But we do not have the base of the triangle, which is one of the sides of the right triangle, so we can calculate it using the Pythagorean Theorem
Where
$c=1200ft$
$h=a=1000ft$
$c^{2}=a^{2}+b^{2}$
$b=\sqrt {c^{2}-a^{2}}$
$b=\sqrt {(1200ft)^{2}-(1000ft)^{2}}=663.33ft\approx663ft$
So,
$A=\frac{bh}{2}=\frac{(663.33ft)(1000ft)}{2}=331,662ft^{2}$
So the total area is:
$A_{total}=965,142ft^{2}+331,662ft^{2}+1,800,000ft^{2}=3,096,804ft^{2}$
But we are asked to find it in acres.
We know that $1 acre = 43,560ft^{2}$. Thus, we have:
$A_{total}=3,096,804ft^{2}*\frac{1acre}{43,560ft^{2}}=71.1~acres$
