Geometry Questions

1 point Perform the following operations on the vectors 2 2 2 3 2 5 and 4 5 2 6 6 u 12 v vw

For the rhombus below find the measures of 21 22 23 and 24 3 2 57 m 2 1 m 22 m 43 m 24 D 0 0 0

The tin can shown at the right has the indicated dimensions Estimate the number of square inches of tin required for its construction HINT Include the lid and the base in the result 1 1 2 in 4

21 Find the exact perimeter and area of the segment shown given that mo 60 and OA 12 in Exercises 21 22 A B

For each figure below determine by using the markings if there is a pair of congruent triangles If there is name the congruen justifying the congruence Note that the pairs of triangles are drawn as congruent but you should not rely on how they are drawn in determining your answers If necessary you may learn what the markings on a figure indicate a U W b Z AA L AV E K O Not Necessarily Congruent Congruent A UVWA by the Choose one O Not Necessarily Congruent O Congruent A ABC Aby the Choose one O Not Necessarily Congruent O Congruent A GHIA by the Choose one A

3 In the semicircular region shaded DQ a Find the exact perimeter of the region b Find the exact area of the region C Q Exercises 3 4 D 6

6 If the area of the circle is 360 in what is the area of the sector if its central angle measures 90

10 Find the exact length of minor arc CD 12 cm C 135 12 cm D

5 In the circle the radius length is 10 in and the length of AB is 14 in What is the perimeter of the shaded sector B Exercises 5 6

7 Find the exact lengths of the radius and the diameter of a cir cle whose area is a 257 in 2 b 2 257 cm 1

2 Find the exact circumference and area of a circle whose diameter has length 10 in

4 Find the approximate circumference and area of a circl whose diameter has length 20 cm Use 3 14

Order the side lengths IJ JK and KI from least to greatest Note that the figure is not drawn to scale 41 K 85 X

In a particular type of regular polygon the length of the apo them is exactly one half the length of a side What type of regular polygon is it

5 In a regular polygon each interior angle measures 135 If each side of the regular polygon measures 4 2 cm find the perimeter of the polygon

13 Find the area of a square with apothem a 3 2 cm and perimeter P 25 6 cm 11 Find the area of aquilotoral triangle with anothom

15 Find the area of an equiangular triangle with apothem a 4 6 in and perimeter P 27 6V 3 in 16 Find the area of a sauore with anothom a ft and

4 Find the area of an a a perimeter of 24 6 cm b a radius of length 4 in equiangular triangle with

In Exercises 17 to 30 use the formula A area of the regular polygon described ap to find the 20 Find the area of a regular octagon with an anthem of length

5 Rectangle A is dilated to form rectangle B A 6 e 20 B 30 Target due 10 31 23 39 5 75 What scale factor was used Enter the answer and also provide a 1 sentence explanation that describes how you determined your answer Review the rub you will be evaluated

18 A Find the area 12 B I I I D 20 Kite ABCD C

In Exercises 19 to 22 find the area of the shaded region 19 24 20 1 14 20 12 6

In Exercises 1 to 8 find the perimeter of each polygon 13 in 1 5 in 12 in 2 A B 18 in 7 in ABCD D

7 AABC is an obtuse triangle with obtuse angle A ADEF is an acute triangle How do the areas of AABC and ADEF compare A Exercises 7 8 8 B h 6 D 8 E

0 In a triangle whose area is 72 in the base has a length of 8 in Find the length of the corresponding altitude

24 Carpeting is to be purchased for the family room and hallway shown What is the area to be covered 2 yd 16 ft 2 yd 5 yd 9 yd

5 B A 4 ft 7 ft 13 ft D Trapezoid ABCD with AB DC 6 X 3 5 2x

In Exercises 9 to 18 find the areas of the figures shown or described 9 A rectangle s length is 6 cm and its width is 9 cm

23 A triangular corner of a store has been roped off to be used as an area for displaying Christmas ornaments Find the area of the display section 24 ft

In Exercises 20 and 21 use Theorem 9 2 1 in which the lengths of apothem a altitude h and slant height of a regular pyramid are related by the equation 2 a h 20 In a regular square pyramid whose base edges measure 8 in the apothem of the base measures 4 in If the height of the pyramid is 8 in find the length of its slant height

13 Assume that the number of sides in the base of a pyramid is n Generalize the results found in earlier exercises by answering each of the following questions a What is the number of vertices b What is the number of lateral edges c What is the number of base edges d What is the total number of edges e What is the number of lateral faces f What is the total number of faces Note Lateral faces and base faces

5 In the solid shown base ABCD is a square a Is the solid a prism or a pyramid b Name the vertex apex of the pyramid c Name the lateral edges d Name the lateral faces e Is the solid a regular solid E A B Exercises 5 7 9 11 C M S V N R P Exercises 6 8 10 12

a Base Exercises 14 15 5 In the regular pentagonal prism shown above suppose that each base edge measures 9 2 cm and that the apothem of the base measures 6 3 cm The altitude of the prism measures 14 6 cm a Find the lateral area of the prism b Find the total area of the prism

17 For the right triangular prism found in Exercises 16 17 Exercise 16 suppose that the sides of the triangular base measure 3 ft 4 ft and 5 ft The altitude is 6 ft in length a Find the lateral area of the prism b Find the total area of the prism c Find the volume of the prism

Exercises 1 3 5 7 9 7 Suppose that each of the bases of the hexagonal prism in Exercise 1 has an area of 12 cm and that each lateral face h

centimeters in I cubic meter 19 Given that 12 in 1 cubic foot 1 ft find the number of cubic inches in

The units are in yards 612 2 What is the measure of the radius of this circle T yd What is the area of this circle A Tyd 3 Explain the process you went through to determine the measure of the radius for the BiU U Font Family AA A PHN F

2 Draw the altitude of the triangle from vertex A O O B B B C OPTIC B B

5 O 10 What is the measure of the radius of the SMALL circle T Small Circle What is the area of the SMALL circle Asmall Circle ft ft What is the measure of the radius of the LARGE circle Large Circle ft What is the area of the LARGE circle ALarge Circle What is the EXACT area of the shaded region Am f42

EXTRA CREDIT The units are in yards Find the area of the shaded region Ashaded Region Tyd

B X 18 8 P X Solve for x x 9 PQ is a Mid segment of A ABC A ABC A APQ 7 Since the Triangles are Similar we can use Proportions to solve for x 8 We can solve this proportion by CROSS MULTIPLYING 9

10 What is the measure of the radius of this circle mm What is the area of this circle Acircle TMM What is the area of the square mm Asquare What is the EXACT area of the shaded region Ashaded Region mm

REDIT The units are in yards Find the area of the shaded region Ashaded Region Tkm

6 Which of the following could the segment AB NOT be B O Perpendicular Bisector O Angle Bisector O Median Altitude Mid Segment

1 The units are in miles 10 What is the measure of the radius of this circle T mi What is the area of this circle A TMi

1 Draw the angle bisector on the triangle from vertex A O O O B B B C OPTIO

3 Draw a perpendicular bisector of the triangle O esc B B 8 O F1 F2 OPTIC B

Graph y x 2 and y 3x on the same set of coordinate axes Use the graphs to find the exact solutions to the equation x 2 3x Then find the solutions using an algebraic method

7 Given isosceles trapezoid ABCD with AD BC AB 24 DC 12 m A 45 Find the area of the trapezoid A D 12 E C F 2 points B

4 Find the area of the quadrilateral ABCD AB 15 AD 9 BC 5 CD 13 2 points B 50 C 15 13 A 9