Test 4 (chapters 8 and9) .
Use your new conjectures to solve each problem.
1.
What is the diameter of a circle that has an arc with a measure of 80° and an arc length
of 88,000cm?
2. The circumference of a tablecloth is 100 inches. Will it cover the top of a table with diameter 30 inches?
Explain
Solve each problem below. The figures are not drawn to scale.
3.
h = 16 cm Area = –?–
5.
Area = 756 cm2 a = 39 cm, h = 18 cm, b = –?–
7–10.
4.
The circumference is 36 cm. Area = –?–
6.The area of the sector is 144 cm2. mFAN = –?
Find the are of shaded region. All measurements are in centimeters.
56
4
10
14
5
2
28
7.
11. Find the area.
8.
10
9.
10.
12–13.
12.
Determine the surface area of each figure.
13. Surface Area = __________
14. Al’s Pizzeria sells cheese pizza by the slice according to the figure below. Which slice gives the best deal (the
most pizza per dollar)?
15. Find the apothem of a regular octagon with area of 690 sq ft and side length of 20 ft.
16. Mr. R. E. Claim has built a warehouse to stockpile all of the recycled paper towels and napkins
wasted by BRHS students to help him corner the market. The main storeroom is rectangular, with dimensions 7 m by 9
m by 4.5 m high. The interior surfaces ( event the floor) must be coated with a flame-retardant material that costs
$39.95 per gallon. If one gallon covers 110m2, how much will he have to pay to protect the storeroom?
17. The A of a regular polygon is 125 m 2 , the a = 5 m . Find the perim eter of the polygon.
18. Show how you can find the area of a trapezoid using a parallelograms area of B times H.
1
19. Show that the Area of a regular Pentagon is

A
regularpentagon

sa 5
2
20. Find the surface area. (d on’t forget the insid e and the bottom ). All m easures are in cm .
3
2
10
21. The —?— is the side opposite the right angle in a right triangle.
22. In a right triangle, if x and y are the lengths of the legs and z is the length of the hypotenuse, then —?—.
23. In an isosceles right triangle, if the legs have length x, then the hypotenuse has length—?—.
24. In a 30-60 right triangle, if the hypotenuse has length 2y, then the shorter leg has length —?— and the longer leg has length —?—.
25. Is the following a right triangle?
26. Find x
27. AB = –?–
28. What is the length of the hypotenuse of a right triangle with legs that measure 80 feet and 150 feet?
29. If a right triangle has a length of 15 for the hypotenuse, then what could the length of each leg be?(hint 3-4-5)
30. What is the length of the larger leg of a 30-60 right triangle with a hypotenuse of length 24 m?\
31. If the area of a square is 225 cm2, what is the length of the diagonal?
32. Determine whether ABC with vertices A(2, 4), B(10, 2), and C(7, 7) is scalene, isosceles, isosceles right, or equilateral
using the distance formula.
33. Two jets pass over each other at point A at 10 p.m. One jet travels south at 480 km/hr; the other travels east at 900
km/hr. How far apart are the two jets at midnight?
34. Find the area of an equilateral triangle with sides measuring 6 meters.
35. Find the circumference of a circle inscribed in an equilateral triangle with a height of 12 3 in.
36. Use the grid lines as a guide to turn sAB into the hypotenuse of a right triangle. Then find the length of sAB.
37. Find the shaded area. AB = 6 3 cm
38. A 25-foot ladder is placed against a building. The bottom of the ladder is 7 feet from the building. If the top
to the ladder slips down 4 feet, how many feet will the bottom slide out? No, it is not 4 fet. This is a two-step
problem, so draw it with two right triangles.
39. AB = 10, Find the area of the equilateral triangle. Find the area of the circum scribed circle. Find the area of
the inscribed circle.
A
B
C
Find the Surface Area of each solid. In Problem 44, the base is a trapezoid. All measurements are
in centimeters unless given..
40.
41.
10 ft
7 ft
3 ft
9 ft
8 ft
4 ft
42.
43.
44. Find the surface area of the solid. Measurements are in centimeters. Hint 3-4-5
Answ ers:
1. 126050.71 cm
2. yes, the circum ference of the table is only
94.2 in.
3. 208 cm 2
4. 1017.88 cm 2
5. 45 cm
6. 40 d eg
7. 1231.5 cm 2
8. 21.46 cm 2
9. 62.83 cm 2
10. 7.13 cm 2
11. 46.5 cm 2
12. 471.24 cm 2
13. 224 cm 2
14. [email protected]=9.6
[email protected]=9
[email protected]=9.6 , so
the giant
15. 8.625 ft.
16. 2.45 gallons, so he need s 3 gallons.
$119.85
17. 50m
18. look in notes
19. look in notes
20. 571.8 cm 2
21. hypotenuse
22. x 2  y 2  z 2
23. x 2
24. y, y 3
25. no
26. 24
27. 26
28. 170
29. 9,12
30. 12√3
31. 15 2
32. isosceles right
33. 2040km
34. 9 3m 2
35. 8 3in , 4 3in
36. 5
37. 12 cm 2
38. 8 feet
39.
Atriangle  25 3cm2 ,
Acircumscribedcircle 
Ainscribedcircle 
25
cm 2
3
336cm2
40.
41.
282cm2
42.
307 .6cm2
43. 1556.4cm
44.
100
cm 2 ,
3
2
SA  102cm2