Question

a parking lot is constructed in the shape of a parallelogram if the base is 200 in the height is 120 ft and a diagonal with its 140 what is the area of the parking lot

Answer 1

We can draw the following picture:

then, we can see that the parallelogram consists in 2 equal triangles:

The area of a triangle is

$A_T=\frac{b\cdot h}{2}$

By substituting the given values into the area formula, we get

$\begin{gathered} \\ A_T=\frac{200\cdot120}{2} \\ A_T=\frac{24000}{2} \\ A_T=12000ft^2 \end{gathered}$

Therefore, the area of the parallelogram is twice the area of one triangle:

$A_{\text{parallelogram}}=2\cdot A_T$

which gives:

$\begin{gathered} A_{\text{parallelogram}}=2\cdot12000 \\ A_{\text{parallelogram}}=24000ft^2 \end{gathered}$

that is, the answer is 24000 ft^2