Sliding A Dimension

Geometry Level 1

Imagine a rectangle. Keeping the base firm, if you slide the rectangle from the top to make a parallelogram so that its area is exactly half of that of the rectangle (with same dimensions), what would be the smaller angle of that parallelogram in degrees?

The answer is 30.

1 solution

Victor Paes Plinio
Apr 8, 2016

Look my schematic:

The problem says that the dimensions of the quadrilateral remains the same. Thus the angle $\theta$ is part of a right triangle as in the image.

The sine of the angle is:

$\sin \theta=\frac{\frac{b}{2}}{b}=\frac{b}{2b}=\frac{1}{2}$

And:

$\arcsin ( \frac{1}{2} ) = 30$

Thus the answer is 30 degrees.