# Chapter 10

### Stephanie Windau

## 10.1-Areas of Parallelograms and Trapezoids

## 10.1-- Vocab

**Base of a Parallelogram**-the length of any one of its sides

**Height of a parallelogram**-the perpendicular distance between the opposite side

**Base of a trapesoid**-its two parallel sides

**Height of a trapezoid**- the perpendicular distance between the bases

## 10.1-- Examples

**If the height of a trapezoid is 3m, and b1 is 4 m, and b2 is 8 m, what is the area?**

The formula for a trapezoid is, .5(b1+b2)h, so you would input the numbers so that you can solve the question. The formula is now, .5(4+8)3=A, then you solve, the answer to this question is, A=18m squared.

**If the height of a parallelogram is 3 cm, and the base is 5 cm, what is the area?**

The formula to a parallelogram is base*height=area. You then input the numbers, 3*5=A, then you solve for the area. The area of this parallelogram is 15 cm.

The trapezoid below is the next problem that we are going to solve.

You have the b1, b2, and the height.

Input the numbers into the formula.

.5(10+18)9=A

A=126

## 10.2-Areas of Circles

## formula to get the area and circumference of a circle

## 10.2 Vocab

__The amount of space inside of the boundary of a flat object__

**Area-**** Circle-**a round plane figure whose boundary consists of points equidistant from a fixed point

__ radius- __a straight line from the center to the circumference of a circle or sphere

** diameter-** a straight line passing from side to side through the center of a body or figure, especially a circle or sphere

** circumference- **the enclosing boundary of a curved geometric figure, especially a circle

__ pi- __3.14159265358

## Find the area of the circle

## The answer is ....

## More Examples

Radius=3

Use 3.14 for pi

First you would insert the numbers into the equation- 3.14*(3*3)

then solve- the answer is 28.26

## 10.3- Three-Dimensional Figures

## Vocab

**three-dimensional figure that encloses a part of space**

__Solid-__** polyhedron-**a solid that is enclosed by polygons

** face-**polygons that form a polyhedron

** prism-**a solid geometric figure whose two end faces are similar, equal, and parallel rectilinear figure, and whose sides are parallelograms

** pyramid-**this has one base and the other faces are triangles

** cylinder-**a solid geometric figure with a straight parallel sides and a circular or oval cross section

** cone-**a solid or hollow object that tapers from a circular or roughly circular base to a point

** sphere-**a round solid figure with every point on its surface equidistant from its center

** edge**-the segments where faces of a polyhedron meet

** vertex-**a point where tree or more edges meet

## Examples

*What is this??...*I come with something very sweet. Kids love to eat me after a cold snack. I usually come with Ice cream?

Answer-Cone

*What am I?...*

I bounce very easily. Without me, most sports wouldn't be able to function.

Answer-Sphere

## Answer -

## 10.4(Surface Areas of Prisms and Cylinders)

## Formula

Surface area of a cylinder- 2*2.14*r*r+2*3.14*r*h

## Vocab

**two-dimensional pattern that forms a solid when it is folded**

__net-____surface area- __the sum of the areas of its faces

## Examples

Answer-56,957.1

Find the surface area using B(area of the base),P(perimater of base),and the h(height)

B= 4 inch, P=8 in, h=5 in.

Answer=48 in

## This is what?

## It is a rectangular pyramid

## 10.5(Surface areas of pyramids and cones)

## Formula

**surface area=area of base+(number of triangles*area of each triangle)**

__Surface area of a pyramid using a net-__** Area of a lateral surface of a cone using a net**- A=3.14*r*l

** Surface area of a Cone-**S=3.14*r*r+3.14*r*l

## Vocab

**-the height of a lateral face,that is, any face that is not the base**

__slant height__## Examples

Answer-400 feet

## 10.6(Volume of Prisms and Cylinders)

## Formula

**V=Bh**

__Volume of a prism-__** Volume of a cylinder-**V=3.14*r*r*h

## Vocab

**the amount of space it occupies**

__volume-__## Examples

r=4 ft., h=11 ft.

answer-552.9

find th volume of the rectangular prism with lenth, width, and height

l=6 m., w=2 m., h=11 m.

answer-132 m3

## 10.7-(Volumes of Pyramids and Cones

## Vocab

**this is a polyhedron. Pyramids have one base. The other faces are triangles**

__pyramid-____cone- __a solid with on circular base

__volume-__ a measure of the amount of space the solid occupies

## Examples

## 10.8(volume of a sphere)

## Vocab

**A measurement of how much space the solid occupies**

*volume-***sphere-**a solid formed by all points in space that are fixed same distance from a fixed point called the center

## Examples

The sphere below shows a sphere with the radius of 14. What would be the volume of this sphere?