Area Questions and Answers

What equation will help you find the distance d between the two points pictured here 4 1 2 2 1 d O 2 1 d O 1 2 d 01 2 d 2 2 A 2 4 X

Expense Gas Insurance Oil Registration Depreciation Yearly cost or rate 500 00 400 00 100 00 100 00 20 What is the cost per mile over the course of a year for a 20 000 car that depreciates 20 with costs shown in the table and that has been driven for 10 000 miles A 0 26 per mile B 1 11 per mile C 4 11 per mile D 0 51 per mile

of transformation that ta 5 describe Sequence trapezoid ABCD to TSEU DOK MICK the sequence a

The plane region bounded by the curve y 1 is revolved about the line 2 Find the volume of the solid generated Select one 32T 3 16T d cubic units cubic units 2 cubic units 3 4T cubic units 8T cubic units

T 6 AT and AC are tangent lines to circle O The length of AC is 3 3 The length of AO is 6 You are playing Pin the Mouth on the Party Guy What is the probability you completely fail pin the mouth nowhere on the face aka on the party hat only A

8 Find the area of the shaded pieces 20 10 in 3 652 in

Find the area of the region f 1 x sqrt x 2 1 pi

18 The diagram shows a vertical tree PQ and two observers at A and B standing on horizontal ground AQ 25 m QAP 37 QBP 42 and AQB 75 a Find the height of the tree h P 48 25M 4278 the distance between the two observers Smks

length of each arc Round your answers to the nearest tenth 12 240

What is the approximate arc length in a circle with radius of 31 4 inches and arc measure of 82 Round both answers to 1 decimal place 1 31 40 82 7 S re Y 31 4 32 14 3 Approx 180 180

Find the measurement of arc FE 20x F 4x 12 E B G C 4x 12 20X 4X 12 16x 16x 16x 75 X 4x D

Calculator What is the value of x Enter your answer in the box X 5 cm 32 cm 40 cm 2 4 cm

Use the diagram below to answer all parts of the q A 32 C B

Find the volume V of the described solid S The base of S is the region enclosed by the parabola y 6 x and the x axis Cros perpendicular to the x axis are squares

Relating Radlans and Degrees The exact number of radians in one half of a circle is w A semicircle has half the circumference C In terms of radians the measure of the central angle is equal to the arc length divided by the radius 8 A semicircle has 180 E 180 T rad There are about 3 14 radians in a semicircle 0 14r

C 2mr or C nd A radian is a central same length as the radius In degrees s Arc length a portion of the circumference of a circle can be found using In radians the distance around the circle is found using where the intercepted arc is the 1 radian r ww

Finding Radian Measure Find the number of radians in one fourth of a circle half of a semicircle or a fourth of 1 2 2 4 1 two thirds of a circle 2 3 Examining Arc Length When r 1 S 0 27 The units for the prel m or If the radius of a circle is equal to 1 0 0 2n S 277 1 S 2 1 H N 2TT 2 2 3 1 3 rad rad Tradians 2 0 0 K 360 S 0 L

Area of a Circle The area of a circle is found by multiplying the times Area is the amount of space inside of a figure All circles are similar because any full circle is measured to be 360 degrees or 2 pi in radian measure The area is only affected by the changes in the radius KO 6 feet Solving Problems Involving Area A fountain with a circular base has a radius of 6 feet and is surrounded by a circular path that has a width of 2 feet What is the total area occupied by the path alone 2 feet r Fountain Find the area of the fountain find the area of the fountain and the path and then subtract them from one another Area of the fountain A A r Area of the path A 6 R of the radius Area of the fountain and path r 36 ft 9 64 ft 367

TULE DIUS 10 the area of the sector central DOS MONETANSARE Words to Know Write the letter of the definition next to the matching word as you work through the lesson You may use the glossary to help you CHERRIMON PERSO VARIND degree seco Minthem OPT S radian DASS AMOUR A Do for BOSTA MRISH SKECH SONG SONGS HAGE angle PHARETLY SATRZAS ELETT Pinces ARMELEG enrised Recor CARLMENTEER INSTAT me ke Analyze the sector of a circle D an angle whose vertex is at the center of a circle whose and sides are radii of that circle CHOLERNISS MARKE a circle veltestant A a standard unit of measure for angles the measure of a central angle that subtends an arc that is equal in length to the radius of the circle of B the region of a circle bounded by two radil and their intercepted arc C a unit of measure used in measuring angles and arcs there are 360 degrees in a circle P HONGE Sicht El de marque HAMAINEE Es Polaget TRAINE PLANT S Pes WANA AME AMPAST SA

An inscribed angle has two Intersecting chords with the vertex and the endpoints on the circle The sides are not necessarily A circumscribed angle is created by two intersecting segments The vertex is outside of the circle The sides are congruent 0

4 7 km km A 5 2 km C 3 km 4 8 km Area 14 7 km B 4 2 km D 5 7 km

41 3 6 km 3 4 km 3 km A 17 1 km C 34 2 km 8 km 4 km B 8 6 km D 20 8 km

10 3 points A water cup in the shape of a cone has a diameter of 8 inches and a height cup is filled with water to half of its height determine the volume of water in the cup to the nearest hundredth of an inch Hint The height and radius are proportional in a cone so if the height is cut in half so is the radius

4 The following represent three different shaped cups I rectangular prism with a square base with a side length of 3 in and a height of 6 in II cylinder with a diameter of 4 in and a height of 3 in III cone with a diameter of 6 in and a height of 5 in Which of the following represents the cups in order of greatest volume to least volume A I II III B I III II C II III I D II I III

Use the scenario below to answer 6 and 7 A rectangular prism fish tank has a base with a length of 40 inches a width of 35 inches and a height of 12 inches 6 If the tank is filled to 75 capacity what is the volume in the tank A 360 cubic inches B 480 cubic inches C 12 600 cubic inches D 16 800 cubic inches 7 Water is removed from the rectangular prism tank such that the water is at a height of 2 inches What is the volume in the tank now A 80 cubic inches B 840 cubic inches C 2 800 cubic inches D 16 800 cubic inches

5 A circular town with a maximum diameter of 4 miles The shaded region represents the water The land is in the shape of a rectangle There are currently 2 052 people living in the town below What is the population density in person per square mile of land A 128 3 B 163 3 C 213 2 D 698 0 4 miles OURIO 3 5 miles s dalwo003 A 2 75 miles

Use 3 14 for pi and round your answer to the nearest tenth Clue 17 What is the volume of this sphere Use 3 14 for T Round yo answer to the nearest tenth 11 cm cm

Based on appearance which names correctly classify this figure Choose ALL that apply Enter capital letters in alphabetical order into the lock A rectangle B square C kite D rhombus E parallelogram F trapezoid

DETERMINE THE AREA Find the area of the right triangle JKL LK 45 JK V180 36 bh 1 1 0 180 HIN V8100 90 units A1 5 10 42 2 2 6 3 0089 Area of A ABC 60 25 6 4 I 2 10 10 6 A V L 2 5 5 4 3 3 S 10 GY 6 10 1122 6 Finding the Area of a Nonright Triangle Using the Box Method Find the area of triangle ABC by finding the area of the bounding box and subtracting the areas of the right triangles surrounding triangle ABC a 52 11s 6 K 4 2 B 3 3 10 4 SS

What is m BCD B 92 O C D 126 m BCD

To find the area of a rhombus or 1 use the Tormula H 1 201 0 To find the length of a segment you can use the d x x y 11 use the formula A d d formula

Finding the Perimeter of a Trapezoid in the Coordinate Plane What is the perimeter of the trapezoid with vertices B 4 4 C 11 4 D 20 10 and E 4 10 Round to the nearest tenth Find CD Find the perimeter 20 18 16 14 12 10 8 6 4 2 CD 2011 2 10 4 81 36 V 2 E B 4 6 P 81 36 29 P B C units 10 12 14 D 16 18 20 X

Finding the Area of a Trapezoid in the Coordinate Plane Using the Box Method What is the area of the trapezoid Area of rectangle B L 12 10 Area of triangle 1 6 12 Area of triangle 2 100 Area of triangle 3 2 4 8 Area of trapezoid 120 36 8 16 20 1 18 16 14 12 10 8 6 17 2 6 x 4 N Draw the box around the trapezoid and label triangles 1 2 and 3 2 41 6 units Finding an Unknown Side Length The area of a trapezoid is 86 86 square inches The height is 17 2 inches and one base is 6 inches What is the length of the other base 1 h d b A 17 2 6 x 173 72 X 8 10 12 14 16 18 20

of the complex figure to the nearest tenth of a cubic meter Do not include units in your final answer 20 m

What area of nickel plating should be used to cover the front of this regular heptagonal coin if the radius is 15 mm and the sides are 13 02 mm Round your answer to the nearest hundredth Draw an apothem to form a right triangle The base of the right triangle is half the length of the side 13 03 2 6 51 Use the Pythagorean theorem to find a a 6 512 15 a 152 6 51 a 225 6 51 Find the perimeter P 13 02 7 Find the area to the nearest hundredth A 225 6 51 13 02 7 D 17 mm 115 3000 G E

RED Assume that the Pentagon in Washington DC is a regular polygon How much land does it cover if the apothem measures about 2882 24 ft and a side measures about 921 ft Find the perimeter Find the area P 921 5 A 1 Zap ft

000 ft below 30 bpm 3 16 above 80 bpm 19 12 31 total 22 28 50 BA 3 The table shows information from the survey about the resting heart rate in beats per minute bpm for 50 people living at altitudes or below 10 000 feet A What is the probability that a person surveyed selected at random has a heart rate above 88 bpm B What is the probability that a person surveyed selected at random has a heart rate above 80 bpm or lives above 10 000 ft

7 Which equation could be used to solve for the missing side sin 28 X 24 X 28 14 cos 28 14 X

9 Find the measure of x and y Y X 80

1 a What is the slope of a line perpendicular to y x 7 b Parallel

CIRCLE A 60 5 CIRCLE B G 78 19 Select ALL the statements that are true The sector in B has a larger area than the sector in circle A account the sectors circles A and B are similar umference taken up by the arc outlining circle A s sector is smaller than the fraction of the circumference taken up by the arc of circle B A s sector to its total area is

Find the value of x A XD 97 89 0

O Cinesa dilation of circle A A b L CHELLE A d CIRCLEA Lanstar U of The ha What is the scale factor of the dilation What the length of the highlighted arc in cle A what is the length of the highlighted arc in circle B What is the ratio of the arc lengths How does the ratio of are length compare to the scale factor that are true 60 5 refin DRCLE CIRCLES O 12 9 9 B 2

Decide whether quadrilateral ABCD with vertices A 2 2 B 2 5 C 2 0 and D 2 3 is a special quadrilateral Select all na hat apply O parallelogram O rectangle O rhombus O square

Determine the area of triangles given in the area coordinate plane Words to Know Write the letter of the definition next to the matching word as you work through the lesson You may use the glossary to help you parallelogram plane right triangle Determine the area of coordinate plane given in the A a quadrilateral in which both pairs of opposite sides are parallel B a triangle having an interior angle measuring 90 degrees C the amount of space enclosed by a two dimensional figure D a system for locating points in two dimensions that uses a horizontal axis and a vertical axis

14 Determine the volume of water inside the figure to the nearest whole number if it s filled 75 with wate 3 ft 8 ft 4 ft 5 ft RP

12 List the volumes from least to greatest 1 Sphere with a radius of 8 in II Cone with a diameter of 6 in and a height of 8 in III Cylinder with a radius of 6 in and a height of 8 in

INDEPEND 1 Below are three different shaped cups Which one can hold the most wa 1 cylinder cup with a radius of 8 in and a height of 4 in II rectangular prism cup with a base area of 9 in and height of 6 in III cone cup with a diameter of 12 in and a height of 4 in Iw mo El a

the lines below parallel Use mathematics to support your claim 0 2 4 10

3 10 What is the center and radius of the circle with the equation x y 14x E 14x 12y 4