Question

An advertising company is designing a new logo that consists of a shaded triangle inside a parallelogram.What is the area, in square units, of parallelogram ABCD?

Answer 1

Explanation:

The complete question is shown in the figure below. As you can see one square units is well shown in the graph. So we can conclude that the distance between two consecutive points is 1 unit. If so, then we can calculate the area of the parallelogram as follows:

$A=b\times h \\ \\ A:Area \\ \\ b:Base \\ \\ h:Height \\ \\ \\ CB=b \\ \\ AB=h$

Then, finding CB by Pythagorean Theorem:

$CB=\sqrt{6^2+4^2} \\ \\ CB=2\sqrt{13}$

And:

$AB=4$

Therefore:

$A=(2\sqrt{13})(4) \\ \\ \boxed{A=8\sqrt{13} \ units^2}$