316 Appendix A
- In trapezoid FIVE, IV FE and mF = 59r. mI = 121r
- In trapezoid TEAR, EA TR and TE = AR. If E = 107r, mA = 107r, and mR = 73r.
- In trapezoid ZOID, ZDOI, mZ = 83r and mI = 97r. If ZO = 4 cm, ID = 4 cm, because ZOID
is an isosceles trapezoid. - In trapezoid PQRT, PT QR and MN is a median.
PT QR MN
2
.
If MN = 17 inches and PT = 21 inches,
.
- For a square with a side of 17 cm, perimeter is 68 cm and area is 289 cm^2.
- For a rectangle 18 inches long and 9 inches wide, perimeter is 54 inches and area is 162 square
inches. - For parallelogram ABCD, AB = CD = 7 inches, AC = BD = 21 inches, and the height from B
perpendicular to AC and AD 3 inches, perimeter is 56 inches, and area is 63 square inches. - For a rhombus with sides 5 inches long and diagonals that measure 6 inches and 8 inches,
perimeter is 20 inches and area is 5 square inches.
(^) A^1 dd
2
1
2
12 68 24
- If the area of a parallelogram with a height of 48 cm is 3,600 square centimeters, the base to
which that altitude is drawn (and the opposite side) must measure 75 cm. If the perimeter is
250 cm, the other two sides each measure 50 cm. - The number of diagonals in an octagon is^85
2
20.
- The total of the measures of all the interior angles in a nonagon is 180 9 2 1260 .
- If a hexagon is regular, the total of the measures of all the interior angles is 180 6 2 720 ,
and the measure of any one of its interior angles is^720
6
120
.
- If the interior angles of a polygon add up to 900r, then 900r = 180r(n – 2), and n – 2 = 5. The
polygon has 7 sides. - If a polygon has a total of 119 possible diagonals,
nn
3
2
119 so n(n–3) = 238. The factors of
238 are 2 v 119, 7 v 34, and 14 v 17. The last pair differ by 3, so n = 17.- The area of a regular pentagon with sides 8 cm long and an apothem 5 cm long is
A ap
1
21
2
5 40 100 cm^2.21
217
21 34
13 inchesQRQR
QR