Chapter 1 - Polygons

Question 1

Sum of the interior angles of a polygon

Answer 1

(n-2)*180

Polygon ** # of Sides ** Sum of Interior Angles

Triangle 3 180

Quadrilateral 4 360

Pentagon 5 540

Hexagon 6 720

Question 2

Area of a triangle

Answer 2

base*height/2

Question 3

Area of a rectangle - All angles are 90 and opposite sides are equal.

To understand the difference between perimeter and area, think of **perimeter as the length of fence needed to enclose the yard, whereas area **is the space inside the yard.

Answer 3

length*width

Question 4

Area of a trapezoid -

1 pair of opposite sides is parallel.

Ex: top & bottom sides are parallel but the right and left sides are not.

Note: base is not necessarily the side that is on the ground. Bases are the two parallel sides and can be vertical

Height is the lenght of a perpendicular line drawn bw the two bases

Answer 4

1/2(Base 1 + Base 2)*height

If a trapezoid has right angle on one side and another right angle on the other side, the sides with the two right angle are parallel to each other and should be used as Base 1 and Base 2 of trapezoid

You can split the trapezoid into 2 triangles

or

1 rectangle and 1 triangle so keep this in mind.

Question 5

Area of a **parallelogram **

Parallelogram is a pair of parallel lines intersected by another pair of parallel lines. When we cross two parallel lines with another line (called a transversal), then we create equal angles. The acute angles (smaller than 90 degrees) will all be the same and the obtuse angles (larger than 90 degrees) will all be the same as well. Therefore, the corresponding acute angles inside or bordering a parallelogram will all be equal and **corresponding obtuse angles inside or bordering will be the same **

Answer 5

base*height

Opposite sides & opposite angles are equal

Any acute angle plus any obtuse angle create consecutive angles are supplementary (equals 180). This is bc we can always put one of the acute angles next to one of the obtuse angles and form a Straight Line.

Question 6

Area of Rhombus -

All sides are equal. Opposite angles are equal

Answer 6

Diagonal 1 * Diagonal 2/2

Question 7

Surface area of a three dimensional shape ( space on the surface of a particular object)

Answer 7

the sum of all of the faces

** rectangular solid and cube have six faces

Question 8

Volume of a three dimensional shape (amount of “stuff” a 3 dimensional object can hold aka capacity).

Another clue is the unit “cubic feet”

Rectangular solid Fact= if the length, width, and height are doubled, the volume will increase by a facor of 8. So if original volume was 10 cubic cm, the new volume will be 80 cubic cm

Answer 8

length*width*height

Question 9

Quadrilateral: Overview

Answer 9

** Parallelogram** (Opp Sides & opp angles are = )

              **       |                                         |**

Rectangle (All angles are 90 Rhombus ( All sides are =
& opp sides are =) & Opp angles are =)

                        * *   |                                 |**
                       * *Square** ( All sides and angles are =)

Trapezoid ( One pair of opp sides is parallel. Ex: top & bottom sides are parallel but right & left sides are not)

Question 10

Perimeter of rectangle

The perimeter of a rectangle is the distance around the outside of the rectangle.

To understand the difference between** perimeter **and area, think of perimeter as the length of fence needed to enclose the yard, whereas area is the space inside the yard.

Answer 10

P= 2L+ 2W or

P= 2(L+W)