Chapter 6.2, Problem 58E

To determine

To find:The area of the parking lot which is in the shape of parallelogram.

Answer to Problem 58E

The area of parking lot is $6577.8sq.m$ .

Explanation of Solution

Given information:

A parking lot has the shape of a parallelogram. The lengths of two adjacent sides are 70 meters and 100 meters. The angle between the two sides is $70°$ .

  

Calculations:

Observing the figure, the area of parking lot ABCD is twice that of the triangle ABC.

So, let’s find the area of $\Delta ABC$ first.

  $\begin{array}{l}Ar(\Delta ABC)=\frac{1}{2}bc\sin (A)\\ =\frac{1}{2}(70)(100)\sin (70°)\\ =3288.9\end{array}$

Conclusion:

Therefore, the area of parking lot is

  $2\times 3288.9=6577.8$ .