Part 3: Geometry

Question 1

What is the equation to calculate the number of degrees in a polygon?

Answer 1

degrees = (n+2)*180, where n is the number of sides.

Question 2

What is the pythagorean theorem?

Answer 2

a^2 + b^2 = c^2, used to determine length of sides in a triangle with one right angle (a right triangle).

Question 3

What is an equilateral triangle?

Answer 3

a triangle where all three sides are the same length (congruent).

Question 4

What is an isosceles triangle?

Answer 4

a triangle where two sides are congruent.

Question 5

What are the ratio of sides in an isosceles right triangle?

Answer 5

a to a√2

Question 6

What are the ratio of sides in an 30-60-90 triangle?

Answer 6

2a to a√3 to a

Question 7

What is the area of a triangle?

Answer 7

(bh)/2, which is base times height divided by 2.

Question 8

What makes for congruent triangles?

Answer 8

All sides are the same. Or one side and two angels are the same. Or one angle and two sides are the same.

Question 9

What makes for similar triangles?

Answer 9

All three angles are the same.

Question 10

What is the area of a quadrilateral?

Answer 10

A = bh

Question 11

What is the area of a trapezoid?

Answer 11

A = 1/2(b1 + b2)h

Question 12

In a circle, what is a chord?

Answer 12

A line segment whose end points touch a circle’s circumference.

Question 13

How to determine the length of an arc?

Answer 13

Given the angle of the arc, the length of the arc can be calculated with the following ratio:
arc angle/360 = arc length/circumference

Question 14

What is the area of a circle?

Answer 14

πr^2

Question 15

What is the area of a sector?

Answer 15

Given the angle of the arc of the sector, the area can be calculated using the following ratio:
area of sector/area of circle = sector angle/360

Question 16

What is special about an inscribed triangle and it’s angle (or side)?

Answer 16

If one of the sides is the diameter of the circle, then it is a right triangle. If one of the angles of an inscribed triangle is 90 degrees, than one of its sides if the diameter.

Question 17

How is a polygon circumscribe a circle?

Answer 17

If all sides of the polygon are tangential, then it circumscribes the circle.

Question 18

What are concentric circles?

Answer 18

Circles that share the same center point.

Question 19

what is the volume of a rectangular solid?

Answer 19

V = lwh

Question 20

What is the surface area of a rectangular solid?

Answer 20

A = 2(lw + wh + hl)

Question 21

What is the a circular cylinder?

Answer 21

Is a can but where the circles can be slid on their respective planes in any direction.

Question 22

What is a right circular cylinder.

Answer 22

A can.

Question 23

What is an axis in a circular cylinder?

Answer 23

It is the line connecting the center of both circles in a cylinder.

Question 24

What is the volume of a can?

Answer 24

V = πr^2h

Question 25

What is the surface area of a can?

Answer 25

A = 2πr^2 + 2πrh

Question 26

Given two parallel lines and two intersecting lines, one of the angles is 57 degrees and the other is 42. What are x and y.

Answer 26

x is also 57 degrees. y is 180-42, which is 138 degrees.

Question 27

Given an isosceles triangle, and an outside angle of 125 degrees, what are x and y?

Answer 27

y is 125 degrees. x is 180 - 55 - 55 = 70 degrees.

Question 28

Given two inside angles x and y and one outside angle z, what is their relationship to each other?

Answer 28

x + y = z

Question 29

What is the sum of the interior angles inside a decagon?

Answer 29

8*180 = 1440 degrees

Question 30

What is a single angle inside of a regular decagon?

Answer 30

144 degrees

Question 31

The lengths of two sides of an isosceles triangle are 15 and 22. What are the possible values of the perimeter?

Answer 31

Perimeter could be 52 or 59.

Question 32

Triangles PQR and XYZ are similar. If PQ = 6, PR = 4, and XY = 9, what is the length of side XZ ?

Answer 32

4/6 = x/9 = 6

Question 33

What are the lengths of sides NO and OP of triangle NOP in Geometry Figure 34 below?

Answer 33

NO = 30, OP = √3400

Question 34

smaller triangle has a area of 42. What is the area of a similar right triangle with a hypotenuse 3 times longer?

Answer 34

42 * 9 = 378

Question 35

Exercise 10

Answer 35

Area of rectangle: 50
Area of triangle: 17.5
Length of diagonal: √125
Perimeter of rectangle: 30

Question 36

Exercise 11. In Geometry Figure 37 below, ABCD is a parallelogram. Find the following.

(a) The area of ABCD
(b) The perimeter of ABCD
(c) The length of diagonal BD

Answer 36

Area: 48
Perimeter: 24 + 4√5
Length of diagonal: √116

Question 37

Exercise 12. In Geometry Figure 38 below, the circle with center O has radius 4. Find the following.

(a) The circumference of the circle
(b) The length of arc ABC
(c) The area of the shaded region

Answer 37

Circumference: 8π
Length of arc: 8/9 π
Area of arc: 16/9 π

Question 38

Exercise 13. Geometry Figure 39 below shows two concentric circles, each with center O. Given that the larger circle has radius 12 and the smaller circle has radius 7, find the following.

(a) The circumference of the larger circle
(b) The area of the smaller circle
(c) The area of the shaded region

Answer 38

Circumference: 24π
Area of smaller: 49π
Area of shaded: 144π - 49π = 95π

Question 39

Exercise 14. For the rectangular solid in Geometry Figure 40 below, find the following.

(a) The surface area of the solid
(b) The length of diagonal AB

Answer 39

Area = 14 + 20 + 70 all times 2 = 208

Length of diagonal: √153