1.Use the Figure Below to Find the Following

1.Use the figure below to find the following:

i) line segment AB

ii) triangle ABC

iii) triangle ABC
2.PQR and ABC are supplementary angles and PQR is eleven times as large as ABC. Determine the measure of each angle.
P+A = 180
P = 11A

Plug the second into the first:

11A+A=180
12A = 180
Divide by 12:
A = 15

Get P:

P = 11*15 = 165

So:

ABC = 15 degrees

PQR = 165 degrees
3.What is the exact area of a circle with a diameter of 29 inches?
210.25 square inches
4.

The following triangles,  ABC and DEF, are congruent.

Find the lengths of all missing sides and measures of all angles for both triangles. Include correct units with each of your answers.

Please fill in the blanks:

First triangle: / Second triangle:
Side AB = 16 cm / Side DF =20 cm
Angle BAC = 37 degrees / Side EF =12 cm
Angle ABC = 90 degrees / Angle DEF = 90 degrees
Angle EFD = 53 degrees

5.Find the area of a trapezoid with a height of 8 m and bases of 10 m and 23 m.
132 square meters

6.A recreation room has the following dimensions. Carpeting will cost $9.00 a square yard. How many square yards of carpet will be needed and how much will it cost? Include correct units at each stage within your solution.

area = rectangle + triangle + square

= 3*8 + ½ * 2 * 3 + 2*2

= 24 + 3 + 4

= 31 square yards

Multiply by the $9 per sq yd

31*9

= $279

7.Find the perimeter and area of a right triangle if the shortest side is 9 in. and the longest side is 41 in. Include correct units with each part of your solution.
Use the Pythagorean Theorem to get the other side:

Sqrt(41^2-9^2)

= 40 inches

Perim – add the lengths:

9+40+41

= 90 inches

Area:

½ * b * h

= ½*9 * 40

= 180 square inches
8.How many cubic centimeters can a cigar box hold if its dimensions are 4 centimeters by 14 centimeters by 12 centimeters? Include correct units with your solution.
V = LWH

= 4*14*12
= 672 cubic cm
9.How many cubic centimeters of ice cream can an ice cream cone (within the cone) hold if its height is 8 centimeters and the diameter of its base is 3 centimeters? Give solution accurate to the nearest hundredth. Include correct units with your solution.
V = 1/3 * pi * r^2 * h

= 1/3 * pi * (3/2)^2 * 8

= approx 18.85 cubic cm
10.Find the approximate value of the volume of the right circular cone with a circular base shown below. Approximate your solution to the nearest hundredth.

3216.99 cubic centimeters
11.In an 8 inch square cake pan and a 9 inch square cake pan, what is the difference in volume each pan will hold? Assume each pan is 1.5 inches high. Show step by step work. Include correct units with your solution.
V8inch = 8*8*1.5 = 96 cu in

V9inch = 9*9*1.5 = 121.5 cu in

Take the difference:

121.5 minus 96

= 25.5 cubic inches

12.For the following floor plan, determine whether it is possible for a person to walk through each doorway without using any of the doorways twice. If it is possible, state such a path. If it is not possible, answer, "not possible."