of the base of triangle ABC, or = 6. Given two sides of each smaller right
triangle, you can use the Pythagorean theorem, a^2 + b^2 = c^2 , to find the length of the third side.
In this case, that third side is the hypotenuse, c, and plugging the given values into the
equation gives (6)^2 + (8)^2 = c^2 , or c^2 = 100, which means that the hypotenuse is exactly 10
inches. The perimeter is the sum AD + DE + EC + AC = 5 + 10 + 17 + 10 = 42 inches, or (E).
42 . H Draw a figure to help you visualize this problem. To find the surface area of a rectangular
box, add the areas of all the faces of the box. In a rectangular box, faces that are opposite one
another are equal, so you can find the area of the front, top, and side of the box and multiply
that result by 2. The area of the front face is 14 × 20 = 280. The area of the top face is 14 × 8
= 112, and the area of the right side of the box is 8 × 20 =160. The total of those three sides
is 280 + 112 + 160 = 552, which is (F). However, this value gives only three of the faces of
the box, so multiply 552 by 2 to get 1,104 square inches, which is (H). If you picked (K), you
may have found the volume of the box rather than its surface area.
43 . C The formula for perimeter of a rectangle is P = 2l + 2w. For this rectangle, the length is three
times the width, or l = 3w. Substituting 3w for l and 32 for P into the formula for perimeter
gives 32 = 2(3w) + 2w, or , 32 = 6w + 2w, 8w = 32, and w = 4. So since the width of the
rectangle is 4 inches, using the relationship l = 3w, the length is 12 inches. To find the area,
use the formula for area of a rectangle: A = l · w = 12 · 4 = 48 square inches, or (C).
50 . F Since you’re looking for the area of the shaded region of the triangular table, you first need to
find the area of the table and then subtract the areas of the circular stands on the inside of the
table. The area of the triangle is A = bh, so you first need to find the height. Draw a line
from one vertex perpendicular to the opposite side, to form two 30-60-90 triangles. Since the
sides of this triangle have a ratio of x:x :2x, and the value of x for this triangle is 10, so the
height of the equilateral triangle is x , or 10 inches. Substitute the base and height into
the formula to get A = bh = (20)(10 ) = (10)(10 ) = 100 square inches. Now find
the areas of the three circle sectors, which are all equal because the circles all have the same
radius. Each of the angles of an equilateral triangle is 60°, so the three sectors have central
angles of 60°. The radius of each circle is exactly half of the side length of the equilateral
