High School Geometry Questions

Multiplication Theorem a How many ways are there to make a list of two different letters among those that appear in COAT b How many ways are there to make a list of two different letters among those that appear in MATHEMATICS c How many ways are there to make a list of two different letters where the first is a vowel and the second is a consonant among those that appear in COAT d How many ways are there to make a list of two different letters where the first is a vowel and the second is a consonant among those that anneer in MATHEMATICS

In order to image small objects with high resolution select all possible methods Lower electron gun current Use a smaller spot size Move up the specimen closer to the objective lens Increase the accelerating voltage Increase the image contrast

To avoid charging effect in SEM imaging select all possible methods Coat with metals Coat with carbon Decrease the voltage Decrease the chamber vacuum Use a larger aperture

Use a graphing utility to graph the function include two full periods Graph the corresponding reciprocal function in the same viewing window y csc 4x 4 y y UU UU 2 2 2 2 y 2 2 2 2 2 y 4 2 X

y csc 2x x 2 111 111 111 111 2 020 14 12 337588 U 111 111 111 III

5m

A point in the figure shaded region A l W 4 17 m 8 m

TT VE 0 5 y 0 5 0 866 The angle 60 is shown in the unit circle Draw in another angle that has the same sin value 0 5 0 60 0 5 0 5 X

What is the volume of the pyramid below 112 116 4

In physics lab Ellie attaches a wireless sensor to one of the spokes of a bicycle w spinning freely on its axle The graph below shows the sensor s height above the ground in centimeters over time t measured in seconds 50 2 75 48 11 75 48 4 P Sensor s height in cm 20 20 20 7 25 38 16 25 38 01 10 11 12 13 14 15 16 1S Time in seconds

12 Find the value of x and y Hint Find x first Then use x to findy x y 5 X 5 4

REASONING In Exercises 29 34 tell whether it is possible for a cross section of a cube to have the given shape If it is describe or sketch how the plane could intersect the cube 29 circle 31 rhombus 30 pentagon 32 isosceles triangle 33 hexagon 34 scalene triangle

10 Parallelogram HIJK 1J HK 18 4 JK d x x HI P A 0 6 H K 4 B B X

In 3 11 Find the indicated information P is perimeter A is area Round answers to the nearest tenths Drawings are not to scale Don t Forget Units 3 11 m 4 X 21 ft 8 1 m P 6 4 m x P A 20 ft

In 1 2 Use Pythagorean s Theorem to find the value of x in each right triangle Round answers to the nearest tenths Drawings are not to scale Don t Forget Units 1 18 in 5 in x X 2 8 in A 36 in 11 in x

Find the area of the kite 6 m B D 42 3 Round answer to nearest thousandths

11 2 In the diagram below DE BC ANI DE and BC DB Write down the values of 11 21 AM MN 11 2 2 DE BC 11 2 3 area AADE area LABC M E 2 4 3

14 In general a cardboard fan with a greater area does a better job of moving air and cooling you The fan shown is a sector of a cardboard circle Another fan has a radius of 6 centimeters and an intercepted arc of 150 Which fan does a better job of cooling you 120 9 cm

As shown below polygon ABCGFED consists of two squares ABCD and CGFE and an equilateral triangle CED The length of BC is 3 cm Determine the perimeter and area of polygon ABCGFED in radical form B a Perimeter h Area 9 A D W

5 Please give exact answers 5 If rectangle ABCD has an area of 64 3 m find its dimensions AC is a diagonal and the measure LBAC is 30 short side length Jonger side lenath

Find the area of the regular polygon 8 9 a hexagon with an apothem of 9 centimeters a nonagon 9 gon with a radius of 1 meter

4 Note Please give all approximate answers rounded to nearest thousandths Keep answers exact in calculator until very end of calculations Round Area answer at the end of your calculations 4 A cup saucer is shaped like a regular decagon with a diameter of 5 5 inches as shown Round to the nearest thousandth a What is the length of the apothem of the saucer b What is the perimeter of the saucer c What is the area of the saucer 5 5 in

Find the area of the composite figure 1 111 6 yd 8 yd 12 yd 2 13 mm T 15 mm 17 mm 8 mm 3 9 cm 2 8 cm 5 2 cm 4 8 cm

3 B A C D FL

Determine whether each pair of tr 13 T W

d Name the postulate if possible that makes the triangles congruent A N B SAS AAS ASA Not Possible M C

A A camper wants to protect her bag of food from bears She decides to tightly stretch a rope between two trees and hang her bag from a point exactly halfway along the length of the rope The first tree is 10 feet east and 6 feet north of her firepit The second tree is 5 feet west and 8 feet north of her firepit The rope is attached at a height of 8 feet to the first tree and a height of 9 feet to the second tree Let the firepit represent the origin movement east of the firepit represent movement in the direction of positive x movement west of the firepit represent movement in the direction of negative x movement north of the firepit represent movement in the direction of positive y and movement above the firepit represent movement in the direction of positive z 1 Write the coordinates of the points on the trees where the rope is attached 2 Find the distance between the points in part a Use sqrt to indicate a square root For example 3 would be written sqrt 3 3 Find the coordinates of the point where the food bag is hung 4 If the food bag is 1 2 feet long when hung and bears can reach a height of 7 5 feet when standing is the camper s food safe from bears Explain why or why not U pointol

8 6 7 km Sm 3 km 7 9 cm 40 cm 9 6 ft J

16 B F

height of the Eiffel Tower Antoine placed a mirror 500 meters away from the tower He then positions himself as shown so that the top of the tower is visible in the mirror He is standing 2 75 meters from the mirror and his eyes are 1 8 meters off the ground How tall is the tower

Jeff is at the position marked X and wants to find the height of the tower shown Viewing from the ground he positions himself so that the top of the flagpole is directly in his line of sight to the tower The flagpole is known to be 18 feet tall Jeff is 20 feet from the flagpole and the flagpole is 40 feet from the tower How tall is the tower Both the flagpole and tower are assumed to be perpendicular to the ground

Jeff is at the position marked X and wants to find the height of the tower shown Viewing from the ground he positions himself so that the top of the flagpole is directly in his line of sight to the tower The flagpole is known to be 18 feet tall Jeff is 20 feet from the flagpole and the flagpole is 40 feet from the tower How tall is the tower Both the flagpole and tower are assumed to be perpendicular to the ground

6 12 in 0 in 22 in 9 in 11 in P A 7 10 f 6 ft P 32 ft A

AB BC CD DE EA P A d x x2 y y2 A B E D

P X A 9 19 7 cm 12 cm x I P X 8 cm A 6 cm

What is the area of the shaded region in the given circle in terms of and in simplest form 60 12 m 1 point O 120 63 m O 96 36 3 m O 120 363 m O 96 6 3 m

What is the area of a regular pentagon with a side of 12 in Round the answer to the nearest tenth 1 point 495 5 in 2 O 311 8 in 2 247 7 in 2 124 7 in 2

What is the circumference of the given circle in terms of 15 in 1 point O 30 in 45 in O 15 in 225 in

Given the regular polygon what is the measure of each numbered angle IN 1 point Oma1 12 mx2 72 Omx1 12 mx2 144 Oma1 36 m2 72 Oma1 36 m 2 144

What is the area of a sector with a central angle of 185 and a diameter of 6 m Round the answer to the nearest tenth 1 point 66 1 m O 5 3 m O 16 5 m O 21 0 m

What is the area of the given circle in terms of 6 6 m 1 point O 16 2 m O 10 89 m O 21 78 m 43 56 m2

13 Write in the necessary angle measures on the diagram then write an equation and solve for x 51 2x 14 799

Question A frustum of a pyramid is a part of the pyramid with two parallel bases The lateral faces of the frustum are trapezoids Use the area formula for a trapezold to derive a formula for the lateral area of a frustum of a regular square pyramid with base edge lengths by and by and slant height 2 B 261 63 201 02

3 As graphed on the set of axes below AA B C is the image of AABC after a sequence of transformations Is AA B C congruent to AABC Use the properties of rigid motion to explain your answer Trans for mation Direction Distanco

Find the value of the trig function indicated 17 tan 7 S 18 cos 5

5 cos 130

5 tan 6 6 09

9 cos 240 1

7 tan 240

3 sin 300 14 cos 6