GEOMETRY DRILL 2 EXPLANATIONS
Plane Geometry
7 . B To solve for the perimeter of a parallelogram, recall that the opposite sides of a
parallelogram are equal in length. The lengths of the four sides of this parallelogram are
therefore 12 m, 10 m, 12 m, and 10 m. The perimeter of the parallelogram is the sum of these
four values, 44 m. If you picked (A), you may have found the sum of the given two sides.
15 . C Since you know that the two lawns have equal areas, you can use the area of Kayla’s lawn to
find the length of the sides of her neighbor’s lawn. The formula for area of a triangle is A =
bh, which means that the area of Kayla’s triangular lawn is A = (90)(80) = (7,200) =
3,600 ft^2 . Using that as the total area of the square lawn, use the formula for the area of a
square to solve for each side. The formula for the area of a square is A = s^2 , where s is the
length of each side of the square. Use the area of Kayla’s lawn to find s^2 = 3,600, and s = 60.
If you chose (E), be careful: this is the perimeter of the square, not its side length.
17 . D When two parallel lines are intersected by a transversal, it forms small angles and big
angles. Any small angle is equal to any other small angle, and any big angle is equal to any
other big angle. Lastly, any small angle and any big angle are supplementary, and their
measures sum to 180°. In the figure, the angle measuring x° is a small angle, and the angle
measuring y° is a big angle, so their sum equals 180°. The other choices make specific
assumptions about the angles, which can’t be supported by the information given in the
problem.
18 . H The question gives the height and total area of Brandi’s triangular wall. To find the length of
the base, use the formula for area of a triangle, which is A = bh. Substitute the given
information to find , 300 = b(6), 300 = 3b, and b = 100 meters, or (H). If you picked (G),
you may have forgotten the fraction in the area formula.
