Polygons & Angles
Area of Polygons
Area
Arc Length
Random
100
What is the measure of each interior angle in a 9-gon?
180(9-2) = 1260/ 9 = 140
100
Find the area of this regular pentagon
ANSWER: 675
There are 5 triangles in this pentagon with a base of 18 and a height of 15
A = b* h /2 = 18*15/2 = 135 units2 per triangle
A of whole shape = 135 * 5 = 675
100
What is the area of a circle with a diameter of 6cm?
Diameter: 6
Radius: 3
Area: pi * 32 = 9pi = 28.26 cm2
100
A circular pool is 25feet in diameter. How many 1 foot tiles are needed to go around the circumference of the pool. (Round UP to the nearest WHOLE tile)
diameter: 25 so radius is 12.5
C = 2pi * 12.5
C = 78.5
ANSWER: 76 tiles
100
Which is greater?
The number of school days left till summer or the number of days in summer break?
ANSWER: Days in summer break
~19 school days left
Summer is ~60 days
200
Given this is a regular pentagon, find the measure of <4
180(5-2) = 540
540/5 = 108 (that's the interior angle)
180 - 108 = 72
ANSWER: 72 degrees
200
You are given two regular pentagons.
Pentagon A has side lengths of 4 in an area of 27.53 in2. If Pentagon B has side length of 12, what is it's area?
Their sides have a scale factor of 3, so the area get's multipled by 9
A: 247.75 in2.
200
A 16" pizza has 10 slices. What is the area of each slice?
diameter: 16 so radius: 8
A = pi * 82 = 64pi BUT since there are 10 slices we divide by 10
AREA of slice = 20.11 inches2
200
Find the arc length of the shaded region
C = 2pi*r (r = 11 since diameter = 22)
C = 2pi*11 = 22pi but since we only want half we have to divide it by two
ANSWER = 11pi = 34.54
200
Why was the circle crying?
It felt pointless
300
In this 9-gon, why is the inside angle 40 degrees?
ANSWER: 40
Method 1: Since a circle has 360 and there are 9 equal triangles that make the full circle 360/9 = 40
Method 2: We can find the sum of all angles 180(9-2) and divide that by 9 to find each angle is 140. That means each angle in the triangle is 70. Since the triangle also adds to 180...
180 - 70 -70 = 40
300
An isosceles right triangle has a hypotenuse of length 20 inches. What is the area, in inches, of this triangle?
ANSWER: 100 or 99.95
You can use 45-45-90 special right triangle or sin, cos, tan to find the base and height are both 14.14
Area: b*h/2 = 14.14*14.14/2 = 99.95
300
What is the area of a circle which has a circumference of 31.4 inches?
C = 2* pi * r
31.4 = 2pi*r (divide both sides by 2pi)
5 = r Now use this to find the area
A = pi*r2
= pi* 52
AREA = 25pi or 78.5
300
Point O is the center of a circle. The measure of arc MP on this circle is 63 degrees. What is the measure, in degrees of its associated angle MOP?
63
300
What famous R&B/Pop singer recently released a Country Album?
Beyonce
400
Solve for the height and base of this triangle
sin(35) = h/10
10* sin(35) = h
h = 5.73
cos(35) = b/10
b = 10*cos(35)
b = 8.19
400
DOUBLE JEOPARDY (if you get the bonus too)!
Hexagon A has side lengths of 6 inches. The perimeter of Hexagon B is 3 times the perimeter of Hexagon B. How long are the sides of Hexagon B?
Bonus: How much larger will the area be?
Sides of Hexagon B are 18 inches
Area will be 9 (32) times larger
400
Juan ate a 30° slice from a pizza with a 18 inch diameter. How much pizza did he eat?
A: pi * 92 = 81pi for whole pizza
but since his slice is 30 deg ...360/30 = 12 tells us that there are 12 slices
ANSWER: 81pi/12 = 6.75pi = 21.2in2
400
A 16-inch pendulum swings through an angle of 40° . How far does the tip of the pendulum travel in a single swing?
r = 16
C = 2pi*16 = 32pi but since it only goes 40* ... 360/40 = 9
ANSWER: 32pi/9 = 11.17
400
What is the diameter of a basketball hoop? (closest answer wins if no one gets it)
ANSWER: 18 inches
500
Find the value of x. 
x = 72.5
500
Jose is painting a fake stop sign as part of his halloween costume. Each side of the stop sign (hexagon) is 4 inches long. How many small tubes of paint must he buy, if one tube can cover only cover 13 square inches?
4 tubes.
(Must round up!)
500
Given the circumference of the circle is 14pi, what is the area of the shaded region?
14pi = 2pi*r so r = 7
Area: pi*72 = 49pi =
ANSWER: 153.9 units2
500
The length of the arc BC is three times as long as the minor arc AB. Given the circumference of the whole circle is 112pi, what is the arc length of minor arc AB?
AB = x BC = 3x and
where x is the arc length of that segment
The whole circumference is
x + 3x + x + 3x = 112pi
8x = 112pi
/8 /8
x = 14pi
ANSWER: 14pi
500
What comes next in the pattern?
1/8, 2/7, 1/2, 4/5,..?
1/8, 2/7, 1/2 (think of this as 3/6), 4/5,..?
NEXT IS 5/4