Area Questions and Answers

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

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

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

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

46 9ft 4ft perimeter and area of each composite figure Round answers to nearest hundredths 2 15cm 3ft P 6ft 49 A 6 cm P 7cm A 2cm

5 3 1 cm P 3 4 cm A 3 8 cm 3 7 cm 13 in 15 in 5 in 2 in P A

Find the area of each circle Use 3 14 for the value of pi Round your answer 1 poin to the nearest tenth Do NOT include units in your answer ie ft in km etc FR 2 in

Find the area of each Round to the nearest tenth Do not include units ie ft in km etc square FR 15 8 m 15 8 m 15 8 m 15 8 m

Find the area of each regular polygon Round your answer to the nearest tenth apothem and picture provided FR 9 6 14

Find the area of each parallelogram FR 8 in 18 in

2 1 cm 10 9 cm 12 9 cm 3 1 c a

1 A roll of wrapping paper covers 25 cm Imani plans to wrap the cylinder below in paper a What is the surface area of the cylinder below b How many rolls of paper will Imani need to purchase 4 cm 2 cm

1 A perimeter and area of each trapezoid Round to nearest tenths Drawings are not to scale 17 in 21 in 16 in 20 in 38 in 2 24 3 cm 8 5cm 9 cm 8 5 cm 9 7 cm 14 4 cm P

10 Parallelogram FTCV Find FT Find CV x x y y Find FC Find TV P y N 6 02

P 15 2 m 20 m 8 7 2 cm 18 8 m P A 12 5 cm 6 3 cm

3 3 5 m P 4 m A 5 8 m 4 P A 4 7 in 5 7 in 6 in

5 r P A 10 cm 7 2 cm 6 18 m 7m X 4cm 8 cm x P A 12m 4 5 m

Find the area of each figure Round to the nearest tenth if necessary Lesson 11 4 18 9 cm 21 cm 19 18 in 12 in 10 in

P A 16ft P A L 9 in

X rays only happen when high energy electrons bombard metals but not for nonmetals True O False

Find the area of the bolded sector Leave your answer exact Your answer will be inform with a and b as integers in reduced form Fill in the blanks with the values of a and b 240 14 km Area square yards a b

01 point I have a full cylinder paint can that I am going to pour my paint into my cone painting bucket Dimensions are below 36 inches 7 8 inches 25 inches 4 inches After I finish pouting the paint from the cylinder to the cone approximately how much paint will be left in the cylinder 274in 238in 286in 291in

8 Given that the area of the quadrilateral ABCD in the figure is 22 5 sq units find the coordinates of D The Ty 11 J A 4 3 B 3 4 T 3 F

8 5 4 D

Prove ABCD is a parallelogram by showing both pairs of opposite sides are parallel given the following points A 2 1 B 1 3 C 6 5 D 7 1

Unit 3 Sample Work Reminder Answer only No x or units for problems with typed response Solve Each Proportion Round to the nearest tenth 6 10 X 6

Geometry BONUS A zip line is constructed across a valley as shown in the diagram What is the width of the valley Must sh work 26 f 102 W 83 ft

8 x y 63 72 1 84

In 6 11 Find the value of each variable drawings are not to scale 6 X 1223 1279 105 1359 98 7 X 65 37 20 a Lo 58

In 3 4 for the given squares find x andy and the length of each side 3 x y 64 12x 3y 4 9y 5 24 X 3y 7

8 For each rectangle find the indicated information 19 M AD 3x 5 BC 5x 9 Find x Find AD Find BC B N LM 3x 7 NO 6x 11 Find x Find LM Find ON O 10 R RU19 2x ST 3x 22 Find x Find RU U Find ST Find RV

Find the value of x Sho 5 14x 28 49 B

13 48 73 55 14 3 cm 5 cm 15 20 64 151 X

17 Find the area of the triangle Round to nearest tenths 110 B Area H 72 ab

ab sin C 18 the missing the area of the triangle Round area to nearest tenths 10 in 15 in 43 V 59 A ZC B Area

Calculate the volume of a square based pyramid with an altitude height of 6 ft and base edges of 8 ft 6 ft 8 ft A B C D 8 ft 64 ft 128 ft 192 ft 384 ft

Question 3 What is the volume of the right cylinder pictured below 10 mm A B D 697mm 80mm 150mm 600mm 6 mm

Find the indicated measure Round to the nearest tenth if necessary 14 The area of a circle is 68 square centimeters Find the diameter SOLUTION

following mzB maE the leg w B 9 cm B E Sem E bare er Versave evested by difacts about X Determine BR

Solve for x Round to the nearest tenth if necessary H 5 4 16 x G

Your Turn 2 A basketball is a sphere 29 5 inches in circumference A baseball is a sphere of circumference 9 0 inches How much material is needed to make a basketball Use 3 14 for fr Round to the nearest tenth 1 How much material is needed to make a basketball Hint C 2mr solve for r 2 How much material is needed to make a baseball Hint C 2mr solve for r

Your Turn Find the surface area of each regular pyramid 1 10 2 6 cm 18 cm EXPLAIN 1B Finding the Surface Area of a Pyramid Read the section below and complete the following activity adapted from Lesson 19 3 If only the height altitude of a square pyramid is given one can use the Pythagorean theorem to determine the slant height The slant height of the square pyramid is the hypotenuse of the right triangle formed by the height and half the base length Recall the Pythagorean theorem formula which tells us that the relationship between the legs and the hypotenuse of every right triangle is a b c where a and b are the legs and c is the hypotenuse Finding the Surface Area of a Regular Pyramid if the slant area is not given Step 1 Find the slant height if it is not given Step 2 Find the lateral area RO Altitute Slant height

3 13 in Your Turn Find the surface area of each regular pyramid Round to the nearest tenth if necessary 1 2 8 ft 6fthed 8 in 8 in right Comp Leave your 6 ft 6 ft EXPLAIN 3 Finding the Surface Area of a Cone Read the section below and complete the following activity adapted from Lesson 19 3 A cone is a solid that has a circular base and a single vertex A right cone is a cone whose axis is perpendicular to the base The surface area of a cone is calculated by adding the lateral area to the base To calculate the lateral area of a right cone the slant height I must be known The slant height of a right cone is the distance from any point on circle of its base to the vertex see figure to the right It is not the same as the height of the cone becord ACCOGLODOG

3 The volume of the cone is given Show the work necessary to find that the volume of the cone is V 78 776 3 mi Use 3 14 for I Show the work 28 mi lup 100 mi 4 Find the volume of the cone be wel stumises 14 m 14 m

Find the volume of each cone 1 Find the volume of the ice cream cone in cubic inches Use 3 14 for and round to the nearest tenth 2 Find the volume of the cone Use 3 14 for and round to the nearest tenth 24in 3 9 in

Your Turn Find the volume of each sphere Use 3 14 for and round to the nearest tenth 3 A spherical water tank has a diameter of 27m How much water can the tank hold to the nearest cubic meter U T 609M 3800 4 The diameter of an NBA basketball is about 9 inches How much air can it hold in cubic inches SPA

on Pizza You are ordering pizza and you have two choices a slice of pizza from an extra large pizza with a diameter of 22 inches or an entire personal size pizza that has a diameter of 6 inches VS The slice costs 4 95 and the personal size pizza costs 3 75 Assuming that the extra large pizza is cut into 8 equal slices will you get more pizza for your money by buying one slice of the larger pizza or by buying the personal size pizza 1 Find the area of the slice of pizza Use 3 14 for T Round to the nearest hundredth 0 5 point 2 Find the area of the personal size pizza Use 3 14 for I Round to the nearest hundredth 0 5 point

1 A circular swimming pool has a diameter of 20 feet To the nearest square foot what is the smallest amount of material needed to cover the area of the surface of the pool Use 3 14 for T

For 13 14 give your answer in two forms 1 in terms of rr and 2 using 3 141 the nearest tenth 13 Find the arc length of AB Lesson 16 2 1 point 80 7 in 285 B 14 Find the sector area of the figure below Lesson 16 3 1 point 10 m

arning Goal from Lesson 16 1 16 2 and 16 3 can determine the relationship between an arc intercepted by an angle and the radius can determine arc length and describe radian measure in terms of proportionality I can determine and apply the formula for the area of a sector 11 The diameter and center of circle C are shown Use 3 14 for 7 Round to the nearest a What is the circumference of circle C 0 5 point b What is the area of circle C 0 5 point How I Did Circle one a 50 12 Convert the following degrees into radians Leave your answer in terms of Lesson 16 2 0 5 point each b 125 I got it I m still learning it 18 in