Geometry Questions

Finding the Area of a Right Triangle with Legs Parallel to the Coordinate Axes Find the area of the right triangle ABC A II 1 1 bh 00 units 36 9 h JK 4 2 2 10 A 10 8 6 4 h 10 B 512 1600 G 6 59 10 6 4 2 L 2 5 20 4 6 10 Finding the Area of a Right Triangle with Legs Not Parallel to the Coordinate Axes Find the area of the right triangle JKL d x x 1 37 b LK 4 2 2 5 U 2 10 10 2 b C A 4 13 B 10 10 K 4 2 x

Using the Box Method to Calculate the Area of a Parallelogram Find the area of parallelogram ABCD using the box method Area of rectangle 5 7 35 Area of triangles 1 Area of triangles 2 Area of parallelogram 35 Area V 4 4 3 2 2 2 6 Comparing Areas REAL WORLD CONNECTION units2 A 2 3 Find the area of the triangle using the box method A 300 2 2 1 1 1 2 3 m 10 B 7 6 5 4 3 2 99 D 5 4 3 2 1 A 12 2 2 3 The area of the parallelogram is larger by 1 square meter A L 4 3 m A The community garden has two flower garden plots available for the same price The layout is displayed on a grid where each unit equals 1 meter Based only on square meters which plot is the better purchase Find the area of the parallelogram 3 2 1 2 3 4 5 V 21 4 m h 3m 1 2 3 4 5 8 PEL 2m x 12345678910

What is the missing reason in this proof Use SAS SSS or ASA E H Statements E is the midpoint of DF DJ FH EJEH DE FE ADEJ AFEH Reasons Given Given Given Definition of Midpoint

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

Finding the Area of a Parallelogram in the Coordinate Plane with One Set of Sides Parallel to an Axis Find the area of the parallelogram DEFG A bh A 3 5 6 units AB 8 10 4 0 4 16 AD 210 60 1 144 36 4 2 A lw A 180 20 3600 3 5 D 3 5 3 Finding the Area of a Rectangle in the Coordinate Plane Find the area of rectangle ABCD B 2 A 10 W 6 V E 1 5 3 F5 3 G 0 3 10 4 2 ER E 24 A C D 8 10

he Height of a Parallelogram What is the perpendicular distance between the line segments AB and CD if the area of parallelogram ABCD is 165 square units 10 b AB 225 VB 0 10 10 6 Q 10 F A 165 AB a D 3 4 C 138 AB 0 9 10 2 9 123 165 15 a units 10

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

What is the value of x in Clue 11 Enter the numeric value for x only rounded to the nearest tenth 6x 15 4x

Polygon interior angle sum theorem The sum of the measures of the LE 180 n 2 where is the number of Polygon exterior angle sum theorem The sum of the measures of the polygon one at each vertex is 360 angles of any it gon is of the polygon angles of a

equal siope intercept form do not include any spaces in the equation Write the equation of a line perpendicular to 2x 5y 10 that passes through 10 3

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

1 Directions Find the following arc measures J 3 5 0 127 G F N K D 104 K L L M E 67 This is M mJL mJML mDE mFE mDEF mCFD mDFE II 2 page mKL mLON mOM mKNL mNL 2 4 U 44 T Y 55 X U A D 164 B C V Z 108 S R 25 W mBC mABC mTQ mQR mTS mSQR mRQT II mXVW mVW mYWU II mYU mXW

A regular octagon has a radius of 15 7 ft What is the approximate area of the regular octagon rounded to the nearest tenth Step 1 Make triangles and find the interior angle measure of the polygon Step 2 Make a right triangle using an and find the angle measures of the right triangle 15 7 ft

To find the area of a rhombus or kite you can use a A d d d and d are the lengths of the diagonals F R T Derive the formula In this example the diagonals are RT and QS d HIN d T bh A Add the areas of the top and bottom triangles 1 1 A bh 2 2 2 d 2 d 2 d 2 d R Let RT 2 cm and QS 5 cm 2 5 T m S

What is the value of angle A in Clue 9 The below shape is a parallelogram Do not include degrees in your final answer k 20 A 2k 10

Find the Area of a Rhombus in the Coordinate Plane What is the area of the thombus Use the distance formula to find the lengths of the diagonals KM 14 4 2 12 232 102 102 200 2 100 LN 12 6 1 10 2 6 4 62 P 72 36 x 2 A 10 2 6 2 18 16 14 12 13 4 A 2 019 K 2 1 F 14 12 12 4 10 12 14 16 18 29

A formula for the area of a regular polygon is A 2 length HE a is the where p is the To find missing lengths draw a Then use the Pythagorean theorem or trigonometric ratios triangle using a radius and apothem

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 To find the area of a trapezoid you can use a h b b 5 6 9 units D b b 6

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

Finding the Area of a Trapezoid in the Coordinate Plane USE DISTANCE FORMULA TO FIND LENGTHS What is the area of the trapezoid d x x QT 191 5 8 RS 12 6 0 1 RU 7 6 2 7 1 DETERMINE THE AREA What is the area of the trapezoid QT 333 RS 37 RU 37 1 A h b b 1 37 333 37 A units 20 18 16 14 12 10 8 6 4 2 20 18 16 14 12 10 B 6 4 2 y Q 1 8 y U 7 7 LAT Q 1 8 1 R 6 1 S 12 0 X 24 6 8 10 12 14 16 18 20 T 19 5 U 7 7 T 19 5 R 6 1 S 12 0 x 2 4 6 8 10 12 14 16 18 20

Directions Find the value of x 7 J 31 K N M L 9 E A F 01 21x 9 C 9x 23 27 B X X 8 16x 13 p S T D R 10 Given CH bisects ZDHG mGF 2x 6 and mDC 7x 1 E 83 G X H X Gina Wilson All Things Algebra LLC 2015 2019

What is the length of x in clue Clue 8 Just write the value do NOT include x A X 15 B

6B 28 Given the quadrilateral on the right Create a circle that touches each vertex Identify the center and radius of the circle you created Write the equation of the circle you created 104 47 4 32 3 N 40 A K

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

Step 3 Use trigonometry to write expressions for the missing lengths Find a and b cos 22 5 a 15 7 cos 22 5 sin 22 5 h 15 7 Find the perimeter sin 22 5 P 15 7 sin 22 5 2 8 15 7 sin 22 5 16 Step 4 Find the area of the polygon 15 7 cos 22 5 15 7 sin 22 5 16 22 5 15 7 ft

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

D A radius of a regular polygon is a segment from the The base of the right triangle formed is half the length of the side 8 2 2 J Use the Pythagorean theorem to find a a 4 1 72 Find the perimeter Find the area cm S Q 49 4 1 a 49 4 1 P 8 2 5 49 4 14 8 2 5 8 2 cm cm to a vertex 7 cm

Warm Up 3 Area of Regular Polygons Words to Know polygon radius of a regular polygon in a plane a closed figure formed from three or more line segments such that each segment exactly two other segments one at each and no segments with a common endpoint are collinear a segment that extends from the regular polygon to a of the polygon a polygon that is both equiangular and

5A 5B 24 A contractor is making a toy model grain bin Suppose the two dimensional figure is rotated bout the vertical axis Each small square in the grid represents 1 square foot a 5A Sketch the three dimensional solid that would be formed b 5B Find the volume of the toy model

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

A regular octagon has an apothem of 12 1 inches and a perimeter of 80 inches What is the area of the octagon 12 1 80 40 12 1 in 12 1 in

Recall that a regular polygon can be broken up into congruent isosceles triangles Find the measure of each central angle 360 8 Find the measure of each base angle of the isosceles triangles 180 central angle 2 180 45 2 11 135 2 Regular Octagon 67 5 45

A 27 Which a b C d e sequence of transformations takes the graph of y k x to the graph of y Translate 1 unit to the right reflect over the x axis then scale vertically by a factor of 2 Translate 1 unit to the left scale vertically by 2 then reflect over the x axis Translate left by 2 then translate up 1 unit Scale vertically by 2 reflect over the y axis then translate up 1 unit Reflect over the line x 1 2 then translate 1 unit to the left k x 1

What is the answer to clue 5 Enter the value of x only do not include x Clue 5 Given DH EG Solve for x D x E H 5 G 12 10 F x

What is the value of the star and the heart in Clue 4 Enter the star then the heart with a comma in between Do not include spaces i e a b Clue 4 Determine the values of a and b in this triangle Record the value of each shape The lock will ask for two or more values 45 2 6 a b

5 occurred to the triangle y K 5 4 3 2 1 1 2 L G 2 3 MathBus com

BB 23 The table shows data from the science fair experiment that studied the number of eggs that hatched at three different temperatures What is the probability that an egg hatched a b What is the probability that an egg hatched or it was kept warm Give an example of two events that are independent of each other hatched not hatched i cool 6 19 room temperature 14 warm 23 2

What is the value of x in clue Enter the value rounded to the nearest tenth X

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

BA 22 100 North High students were asked about their classes this semester Are you in PE and are you in band The responses are recorded in the Venn diagram a How many students are in band b What does the number 20 represent PE 35 20

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

8A 20 List all possible outcomes for spinning the spinner and rolling a fair die Make a tree diagram table or just a list 8A 21 What is the probability of spinning a Y and rolling a 3 X Z Y

2 Classify the triangle Using une best name 130 20 7

9 Find the measure of x and y Y X 80

3 Write an equation be used to solve for x given the segments A 9x 7 39 B 3x 20 C

6 Identify the center and radius of the circle given x 9 y 7 8

8 Name the angle in 4 different ways 2 D7

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