ok, i'm going to assume you don't need help with region Q.
with the other regions, there are two approaches that i think are easier than most others. here they are:
* use the formula for the area of a triangle, (1/2)(base)(height).
just be aware that "base" may not necessarily be horizontal, and that "height" may not necessarily be vertical.
for region P, the base is 4 (extending from (0, 1) to (4, 1)), and the height is 1 (easiest to visualize when drawn from (2, 2) downward, hitting perpendicular at (2, 1)). so area = (1/2)(4)(1) = 2.
for region S, the base is 3 (extending from (5, 1) to (5, 4)), and the height is 1 (easiest to visualize when drawn from (4, 3) rightward, hitting perpendicular at (4, 4)). so area = (1/2)(3)(1) = 1.5.
you can break R up into 2 triangles, each of which has base 2 and height 1.
* break P, R, and S up into "half rectangles".
for instance, split P** up by drawing a vertical line from (2, 2) to (2, 1).
the left half is exactly half of a 2x1 rectangle, so its area is 1.
the right half is exactly half of another 2x1 rectangle, so its area is 1.
the total area is 2.
you can do likewise with regions R and S.
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** "split P"! ha!
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Source: Beat The GMAT — Problem Solving |
Ron has been teaching various standardized tests for 20 years.
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Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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Pueden hacerle preguntas a Ron en castellano
Potete chiedere domande a Ron in italiano
On peut poser des questions à Ron en français
Voit esittää kysymyksiä Ron:lle myös suomeksi
--
Quand on se sent bien dans un vêtement, tout peut arriver. Un bon vêtement, c'est un passeport pour le bonheur.
Yves Saint-Laurent
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Learn more about ron
Another way to solve for R:
R is a square and therefore a rhombus. Area of a rhombus is (d1 * d2) / 2 [d1, d2 being the diagonals].
Each diagonal is 2, hence area is 2.
R is a square and therefore a rhombus. Area of a rhombus is (d1 * d2) / 2 [d1, d2 being the diagonals].
Each diagonal is 2, hence area is 2.
