Struggling a bit with Plane Geometry? Here are all the formulas you’ll need to know to solve for area on the GMAT! You’ll see several shapes, but the most common is the triangle.
To find its area, we use the formula A = ½ bh, where b = base and h = height. The base and the height of the triangle must always form a 90 degree angle. Keep in mind that the height can be inside or outside the triangle.
For a circle, the formula is: A = ?r2. Remember that the radius is half of the diameter. A common simple math mistake students sometimes make is to square the diameter rather than the radius.
To find the area of a square, we use the formula A = s2, where s = side of the square. To find the area of a rectangle, we use the formula A = lw, where l = length and w = width.
To find the area of a parallelogram, we use the formula A = bh, where b = base and h = height. We do NOT multiply the two side lengths. Remember the base and the height must be perpendicular.
To find the area of a trapezoid, we use the formula A = h(b1 + b2) / 2. We essentially take the average of the two bases, and multiply it by the height. Again, the height is perpendicular to each base. Let’s look at a GMAT question involving area:
Is the area of regular parallelogram ABCD ? 16?
(1) Angle BAD = 60
(2) AB = 4
The correct response is (B).
A “regular” parallelogram is a rhombus, meaning all four of its sides are equal (think of it like a square that is tilting to one side).
The formula for the area of a parallelogram is A = bh. Since it’s a “regular” parallelogram, we know the base is 4. The height is the length of the altitude (here drawn in blue). The question asks whether (BE)(AD) ? 16. Let’s plug in AD = 4 and simplify:
(BE)(4) ? 16
BE ? 4
In order for the answer to the question to be “yes,” BE must be at least 4. However, since it is one leg of a right triangle with a hypotenuse of 4 (triangle ABE), there is no way BE can be 4. It must be smaller than 4. The answer to the question will always be “no.” Therefore, Statement (2) alone is sufficient.
Remember that even the most intimidating irregular shape on the GMAT can be broken into smaller recognizable shapes. If you have an odd-looking 5-sides figure, you can probably break it into a triangle and a rectangle – and sometimes you can use your knowledge of special right triangles to find the measurements of the sides! Always keep an eye out for these so-called “hidden triangles” as you prep!
Vivian Kerr is a regular contributor to the Veritas Prep blog, providing tips and tricks to help students better prepare for the GMAT and the SAT.