2D Geometry Questions and Answers

C 16 O O A 108 sin 108 40 sin 108 16 sin 108 40 sin 108 40 sin B 16 sin B 32 sin C 16 sin C 108 40 B

3 7 01 You are planting a garden in the shape of an equilateral triangle as shown in the diagram You want to find the area of the garden to determine how much topsoil you will need 60 6 ft 6 ft 30 6 ft 19 Substitute the values of b and h in the formula A 2 b 1 b h for the area of the garden

A 25 foot ladder leans against a wall so that it is 20 feet high at the top The ladder is moved so that the base of the ladder travels toward the wall twice the distance that the top of the ladder moves up How much higher is the top of the ladder now Hint L t 15 2x be the distance from the base of the ladder to the wall 2x Save Exit The top of the ladder is feet higher now L

An 80 foot rope from the top of a tree house to the ground forms a 45 angle of elevation from the ground How high is the top of the tree house Round your answer to the nearest tenth of a foot feet

Find the value of b Round your answer to the nearest tenth B 40 10 12 A

Write sin 49 in terms of cosine sin 49 COS O

Find the exact value of x X 10 X 6

6 AB is tangent to circles P and Q below If AP 5 AZ x 4 BZ x and BQ 3 Determine the length of PZ in simplest radical form 5 N B

1 AE is tangent to circles D and C If EB x 8 DE 8 AB 6 and AC x a Find DB in simplest radical form b Find the length CB E B

4 In the figure d e and fare parallel lines What is the value of x x 20 70

Solve for x 1 19 3 30 33 X 16 2 4 X 16 5 22 9 2 25 16 1 2 3 4 5 6 7

Organizers of an outdoor concert will use 320 feet of fencing to fence off a rectangular VIP section What is the maximum area that they can fence off 4x X A 6 400 square feet B C 12 800 square feet E 25 600 square feet D 24 000 square feet 3 200 square feet

Which solid figure is represented by this soup can x A cone B rectangular prism C cube D cylinder Mer ar Roth Thank Me QUALITY

Which solid figure is represented by this globe X 1x A cylinder B cube C cone D sphere G G G

To indirectly measure the distance across a lake Lauren makes use of a couple landmarks at points L and M She measures KO OM and NO as marked Find the distance across the lake LM rounding your answer to the nearest hundredth of a meter M L 95 m Diagram is not to scale 109 5 m 125 m K HANDM

2 The town of Manchester population 50 000 has the shape of a rectangle that is 5 miles wide and 7 miles long Part A What is the population density in people per square mile in Manchester Round your answer to the nearest whole number of people per square mile Part B The town of Manchester contains a business area in the center of town that has the shape of a disk with a radius of 1 mile If no one resides in the business area what is the population density in Manchester in people per square mile outside of the business area Round your answer to the nearest whole number of people per square mile

5 A scale drawing of Corinne s bedroom floor is shown below All given dimensions are in feet All intersecting line segments shown are perpendicular Corrine wants to completely cover the floor with square hardwood tiles Each tile has a side length of 1 foot and no tiles will be cut How many tiles will Corinne need to cover the floor 5 69 63 C 79 84 11 6 9

LL F E G Your Answer D If E 33 and D is 63 what is the measure of arc FED

M N P MQN is 12 and arc OP is 137 What is the measure of arc MPO Your Answer

S R Your Answer Q Not drawn to scale If PQ 9 and OP 8 QR 8 find the length of SR Round your answer to one decimal place Sign out Fel

A Question 10 1 point Retake question K N Your Answer M If LM 4 and KL 14 find the length of MN Round your answer to one decimal place

A B C From ZC side AB is the opposite adjacent hypotenuse

1 What is the sum of the measures of the interior angles of an octagon 2 What is the sum of the measures of the interior angles of a 25 gon 360 3 What is the measure of each interior angle of a regular hexagon 30 4 What is the measure of each interior angle of a regular 16 gon 5 What is the sum of the measures of the exterior angles of a decagon 6 What is the measure of each exterior angle of a regular 30 gon 13 FOKUS Que 7 An exterior angle of a regular polygon measures 22 5 How many sides does it have 8 An interior angle of a regular polygon measures 170 How many sides does it have

18 Find m BCA 9x 1 A B 5x 12 10x 37 C

16 Find m2V S X 9x 19 7x 3 T 128 W 111 V U 5r 8

17 If the figure below is a regular polygon find the value of x 9x 18

12 Find the value of x 87 105 xo 135 92 work

D rectangle trapezoid quadrilateral parallelogram rhombus What is the measure of an interior angle of a regular 10 gon C D A 80 B 36 216 144 In parallelogram WXYZ find the angle that is congruent to ZXWZ X A ZXYN B ZXNW C ZXWN D ZXYZ N Z Y 16 What must the values of a and b be for PQRS to be a parallelogram A a 2 b 5 a 4 b 2 B a 17 b 12 4x X Find the value of the variables D 100 2y C D 16 not enough information 6x 8 B y 17

True or false If both pairs of opposite sides of a quadrilateral are congruent then the quadrilateral is a parallelogram A True B False Classify the figure in as many ways as possible A rectangle quadrilateral parallelogram B rhombus trapezoid quadrilateral parallelogram C rectangle square quadrilateral parallelogram rhombus D rectangle trapezoid quadrilateral parallelogram rhombus 133 How many sides does a polygon have if each exterior angle measures 18 Items 2 3 Quadrilateral PQRS is shown 4a 1 R 15 6b P B Q 6x 13 2a 9 7x 5 114 What must m4QPS be for PQRS to be a parallelogram A 18 B 59 a 17 b 12 C D S C 116 10 What must the values of a and b be for PQRS to be a parallelogram A a 2 b 5 a 4 b 2 not enough D 121 not enough information

PQRS is a kite Find the value of x A 122 B 22 2 C 3 D 4 115 S 5x 4 7x 2 R Complete the statement If both pairs of opposite sides of a quadrilateral are then the quadrilateral is a parallelogram A perpendicular B congruent C adjacent

1 2 3 W a Y 12 M 13 K 16 12 34 L B 5 C X cos A sin A sin W tan A cos W tan W sin L cos L tan L as a fraction in simplest form sin C cos C sin X tan C cos X tan X sin M cos M tan M

2 Jake leaned a 12 foot ladder against his house If the angle formed by the ladder and the ground is 68 how far from the base of the house did he place the ladder 13 A ramp is used to load suitcases on an airplane If the cargo door is 7 feet from the ground and the angle formed by the end of the ramp and the ground is 25 how long is the ramp

6 4 x 21 26 Solve for x Round to the nearest tenth 5 19 28 7 32 41 55 8

1 Use rectangle ABCD as shown below for both Parts A and B Decide which value best completes each statement 18in B 15in A 12in Part A The measure of diagonal BD is Part B The perimeter of triangle CDE is E in C D

Find the measure of x P e X 1 4x 3x 3 S R Part 2 Find the measures of PS and QR QR

LMNP is a rectangle Find the value of x and the length of each diagonal LN 7x 3 and MP 4x 3 L P X mLN M N

5 X RECT is a rectangle Find x R 4x12 E x 2 T

2 A 30 60 90 triangle is shown below Find the length of the side labeled y y 60 2 3 30

Graph the points A 5 3 B 1 7 C 1 5 and D 3 1 Draw rectangle ABCD and a Find the midpoints of AC and BD b What appears to be true about the diagonals of a rectangle Draw the rectangle and diagonals Choose the correct answer below OA 10 17 OB 17 O C G O D 2 ZZP K7

The circumference of a circle is 14 inches Find the circle s radius and diameter The circle s radius is 7 inches The circle s diameter is inches

A rectangle has a width of 48 centimeters and a perimeter of 212 centimeters What is the rectangle S The length is cm

Introduction to Piecewise Functions Weight pounds 100 50 T Time months 2 10 Write a piecewise function to describe the graph f x

A meteor crater is 3400 feet in diameter Approximate the distance around the crater Use 3 14 for The distance around the crater is approximately Type an integer or a decimal feet

Find the distance around the figure the figure is mi 4 1 mi 13 mi 16 mi 9 mi

A regular hexagon has a side length of 11 inches Find its perimeter Perimeter

the diagram GH bisects ZFGI Solve for x and find mZFGH 5 Find mZHGI C Find mZFGI a x 9 Simplify your answer mZFGH 24 Simplify your answer b mZHGI 48 Simplify your answer 3x 3

If ST 14 and RT 46 find RS Use the number line below R

4 Figure 2 3 1 3 3 2 1 3 4 aubunitnoo 9130 Function Or Not a function Domain Range Y Intercept Relative Min Relative Max Absolute Min Absolute Max Continuous or Discrete

10 10 pts Determine the set of points in the domain of f t for which f t is continuous Provide mathematical proof for your points of discontinuity using our three criteria hint graph for assistance 1 x f x 2 x x 2 if x 0 if 0 x 2 if x 2

he figure shown for items 4 If XZ 12 what is PZ If XP 3x 2 and PZ 4x 1 what is XP A 11 B 12 C 19 D 22 W X 8 7