Download MAT1002 Week 4 Quiz Key

MAT1002 Week 4 Assignment 3: Quiz
Please give correctly explained solutions for all problems turned in by the due date to receive full credit.
On Day 6, submit your solutions (not simply the answers!) to ALL PROBLEMS to the W4 A3 Dropbox.
It is required that you SHOW YOUR WORK step by step to earn full credit.
On Day 5, post your detailed solutions for the assigned problems in the discussion thread as directed
by your facilitator for review and comments from others. Do not post before Day 5.
Here are symbols you may need:     { } COPY AND PASTE!
1. (4 pts) Use the figure below to find the following:
J
A
H
G
F
B
E
C
D
I
i.
ii.
iii.
iv.
mHBD + mBGI + mGCA = sum of angles in a triangle are 180 degrees
BGC U GCB U CBG = the three angles make BGC
GCB U BH = BGC and GH
ABG U BD = BD and BG
2. (2 pts) A. Find the supplementary angle of 34
180-34= 146
A. 146
(2 pts) B. ABC and PQR are supplementary angles and ABC is eleven times as large as
PQR. Determine the measure of each angle.
A+P = 180
A=11P
11P+P = 180
12P= 180
PQR = 15
ABC = 15*11 = 165
3. (4 pts) Lines l and m are parallel and are cut by the transversal shown. Determine the
measures of angles 1 through 7.
1
29
l
2
3
4
m
5
6
7
3 = 4 = 7 = 29 degrees (by vertical angles and alternate angles)
1 = 2 = 5 = 6 = 151 degrees (by straight lines equaling 180 degrees)
4. (4 pts) Find the perimeter and area of a right triangle if the shortest side is 7 cm and the longest
side is 25 cm.
The other side is sqrt(25^2-7^2) = 24 cm
Perim = 7+25+24 = 56 cm
Area = ½ * b * h = ½ * 7 * 24 = 84 cm^2
5. (4 pts) What is the area in feet of circular tablecloth that has a diameter of 42 inches?
42 inches = 3.5 feet
Area = pi*r^2 = pi*(3.5/2)^2
= 3.0625pi sq ft
C) 3.0625 square feet
6. (2 pts) Find the volume of a refrigerator that is a rectangular solid and is 2 meters tall and has a
base that is 1.2 meters square.
Multiply
2*1.2 = 2.4
B) 2.4 cubic meters
7. (4 pts) A conical water tank has a base with a diameter of 6 ft and is 10 ft tall. How many
gallons of water will the tank hold? Round your solution to the nearest hundredth. (1 cubic foot
holds about 7.480519 gallons)
V = 1/3 * pi*r^2*h
= 1/3*pi*(6/2)^2*10
= 94.2477796 cu ft
= 705.02 gallons
8. (2 pts) Find the volume of a pyramid that has a height of 12 meters and a square base 11 by 11
meters. Include correct units.
V = 1/3 * b*h
= 1/3 * 11 * 11 * 12
= 484 m^3
9.
(2 pts) Find the volume of the figure below with a circular base shown below. Give answer
a. exactly and b. approximated to the nearest hundredth.
12 feet
10 feet
V = pi*r^2*h
= pi*(12/2)^2*10
= 360 ft^2
= approx 1130.97 ft^2
10. (4 pts) a) Find the area of a trapezoid with a height of 6 m and bases of 14 m and 21 m
A = ½*h*(b1+b2)
= ½*6*(14+21)
= 105 m^2
b) Find the perimeter of the parallelogram below.
9 in.
4 in.
5 in.
P = 9+5+9+5 = 28 in
11. (4 pts) A recreation room has the following dimensions. Carpeting will cost $8.00 a square
yard. How many square yards of carpet will be needed and how much will it cost?
5 yd
11 yd
4 yd
4 yd
Area = rect1 + triangle + rect2
= 5*11 + ½*5*4 + 4*4
= 81 yd^2
Multiply by $8:
= $648
12. (7 pts) The following triangles,  ABC and  DEF, are congruent.
A
E
12 cm
13 cm
22.6
F
D
67.4
B 5 cm
C
Find the lengths of all missing sides and measures of all angles for both triangles.
Please fill in the blanks:
First triangle:
Side AB =
Angle BAC =
Angle ABC =
Second triangle:
12 cm
22.6 deg
90 degrees
Side DF = 13 cm
Side EF = 5 cm
Angle DEF = 90 deg
Angle EFD = 67.4 deg
13. (3 pts) Create a graph with five vertices, no bridge, and a loop.