GEOMETRY DRILL 1 EXPLANATIONS
Plane Geometry
8 . F According to the figure, the angle opposite x is 30°, so x = 30. Similarly, the angle across
from z is 40°, so z = 40. Since x, y, and z form a triangle, the sum of these three angles must
be 180°. The value of y is therefore 180 − 30 − 40 = 110°, which is (F).
14 . H Since the area of the six congruent squares is 96, the area of each square is = 16. It might
be tempting to select (F) here, but remember you’re looking for the perimeter of the entire
figure, not the area of each square. The area of a square is equal to s^2 , so the length of the
side of each square is = 4. The perimeter of the figure consists of 12 sides of congruent
squares, so the perimeter is 12 × 4 = 48. Choice (G) confuses the sides of the square with the
sides of the figure. Choice (J) misuses the fact that the figure is 8-sided; (K) finds the
perimeter if all 4 sides of the 6 squares were exposed.
22 . H This question can be approached algebraically or by plugging in your own numbers. If you
plug in some small numbers for the base and height of triangle N, such as 2 and 3,
respectively, the base and height of triangle M would then be four times as big and twice as
big, or 8 and 6, respectively. The area of triangle M would be bh = (8)(6) = 24, while the
area of triangle N would be bh = (2)(3) = 3. Triangle M is therefore 8 times larger than
triangle N, which is (H).
26 . J If the area of the barn is 5,776 square feet, you can take the square root of that number on
your calculator to determine that the sides of the barn have a length of 76 feet. This is also the
length of the corral. The width of the corral is one-fourth its length, so = 19 feet. The area
of the corral is thus 76 × 19 = 1,444 square feet, so (J) is the answer.
27 . C Given GJ is parallel to FK, ΔFHK and ΔGHJ are similar triangles, so they have proportional
sides. ΔGHJ is a right triangle, so you can either use the Pythagorean theorem or identify the
