Question

Find the approximate area of the parallelogram.

Answer 1

As approximation:
4 units * 4 units= 16 squared units

Answer 2

Answer: The area of the given parallelogram is 15 square units.

Step-by-step explanation:  

Let ABCD is the parallelogram shown in the graph in which A≡(-2,-1), B≡(-3,3), C≡(1,2) and D≡(2,-2)

Since, AC is the diagonal of the parallelogram,

Thus, by the property of parallelogram,

Area of triangle ABC = Area of triangle ADC

Since, Area of parallelogram ABCD = Area of triangle ABC + Area of triangle ADC

= Area of triangle ABC + Area of triangle ABC

= 2 ( area of triangle ABC )

Since, the area of triangle ABC

$=\frac{1}{2}|-2(3-2)-3(2-(-1))+1(-1-3)|$

$=\frac{1}{2}|-2(1)-3(2+1)+1(-4)|$

$=\frac{1}{2}|-2-3\times 3 -4|$

$=\frac{1}{2}|-2-9-4|$

$=\frac{1}{2}|-15|=\frac{15}{2}\text{ square unit}$

⇒ Area of parallelogram ABCD = $2\times \frac{15}{2}$

$=\frac{30}{2}$

$=15\text{ square unit}$

Hence, The area of the given parallelogram is 15 square units.