How To Find The Area Of A Region

Past Dominate the GMAT / Apr 05, 2012 / Blog

Finding the Expanse of a Shaded Region on the GMAT

A common GMAT problem solving question asks the test-taker to find the surface area of a shaded region. For case, in the effigy to the right, how would y'all find the surface area of the shaded region?

Unlike finding the surface area of a traditional geometric shape (due east.g. triangle or trapezoid) for which you know a specific formula, in that location won't be a specific formula you'll need to larn to solve these types of questions. The shaded areas tend to be bizarre shapes, equally yous encounter in this figure, and thus a bit of creativity is required on your office.

The expert news for you lot is that the fashion to go about solving these shaded region problems is e'er the same. Instead of trying to find the expanse of the shaded region directly, y'all'll desire to subtract the area of ane of the shapes from the surface area of the other shape(s), and whatever is left over is the area of the shaded region. In other words:

Dominion: To observe the area of a shaded region, subtract the expanse of the smaller figure(due south) (for which you have a known formula) from the surface area of the larger figure (for which you'll also have a known formula).

In the effigy above, for example,

The Surface area of the shaded region = (Area of the largest circumvolve) – (Area of the circle with radius 3) – (Expanse of the circle with radius ii). Whatever is left over is the shaded region.

The diameter of the largest circumvolve is x, so its radius is v and thus its surface area is 25π.

Therefore, the Surface area of the shaded region = 25π – 9π – 4π = 12π

On the GMAT

To gain a deeper understanding of this concept and to see how information technology applies to a existent GMAT question, lookout man this video tutorial about finding the surface area of shaded regions on the GMAT: