Question

A parallelogram has vertices at (5, 3), (8, 4), (7, 8), and (4, 7). What is the approximate area of the parallelogram?

Answer 1

Answer:

13 square units.

Step-by-step explanation:

We can find the area of the parallelogram using the formula:

$Area=2\times \frac{1}{2}[|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|]$

where $A(x_1,y_1)$, $B(x_2,y_2)$. and $C(x_3,y_3)$ are the vertices of one of the triangles created by the diagonals.

$Area=[|x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)|]$

We use A(5, 3), B(8, 4), C(7, 8) to obtain:

$Area=[|5(4-8)+8(8-3)+7(3-4)|]$

$Area=[|-20+40-7|]$

$Area=|13|=13$

The area of the parallelogram is 13 square units.