Lesson: Quadrilaterals

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Hi brent,

Could you please help me understand the approach to solving the following question:

https://gmatclub.com/forum/what-is-the-area-of-rectangular-region-r-166186.html

Is my assumption that diagonals of a rectangle are angle bisectors incorrect?

Is that valid only for square and rhombus?

Thanks in advance!
gmat-admin's picture

Question link: https://gmatclub.com/forum/what-is-the-area-of-rectangular-region-r-1661...

Unless the rectangle in question has 4 equal sides (i.e., the rectangle is a square), then the diagonals do not bisect the angles.

For example, in the following diagonal, you can see that the angles are not bisected:
https://www.math.nmsu.edu/~pmorandi/math112f00/graphics/RectangleWithDia...

As you suggest, the diagonals bisect the angles in squares and rhombuses only.

Cheers,
Brent

Hi, I can't understand the area of a circle: if the area is 4a²π, why the radius is 2a, not 4a? An area of a circle should be Pi (radius)^2? I think I have just missed something..

Image
In the figure above the square has two sides which are tangent to the circle. If the area of the circle is 4a²π, what is the area of the square?

A. 2a²
B. 4a
C. 4a²
D. 16a²
E. 64a²

Thanks in advance!
gmat-admin's picture

Question link: https://gmatclub.com/forum/in-the-figure-above-the-square-has-two-sides-...

We're told the area = 4a²π
NOTE: the a is squared but the 4 is not. That is, the area = 4(a²)π

Take 4(a²)π and make the following EQUIVALENCIES:
4(a²)π = (π)(4)(a²)
= (π)(2²)(a²)
= (π)(2a)²

Since the area of circle = (π)(radius)², we can see that the radius must have length 2a

Does that help?

Here's my full solution: https://gmatclub.com/forum/in-the-figure-above-the-square-has-two-sides-...

Cheers,
Brent

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