# Chapter 10

### Paytyn M

## 10.1

**Vocabulary:***~base of a parallelogram- the length of any one if its sides.*

*~height of a parallelogram- the perpendicular distance between the base and the opposite side *

*~bases of a trapezoid-its two parallel sides*

*~height of a trapezoid-the perpendicular distance between the bases*

## Finding Area of a Parallelogram and Trapezoid

**Parallelogram:***A=bh write formula for area of a parallelogram*

* =8*10 Substitute 8 for b and 10 for h*

* =80 multiply*

*{80 inches squared is the answer}*

**Trapezoid:**

*A=1/2(b1+b2)h Write formulas for area of a trapezoid*

* =1/2(31+77)25 Substitute values for b1, b2 and h*

* =1350 multiply*

*{1350 square feet in the answer}*

## Real Life Examples

## 10.2

**Vocabulary:***~area- the amount of surface the figure covers*

*~circle-is the set of all points in a plane that are the same distance from a fixed point called the center*

*~radius-the distance from the center to any point on the circle*

*~diameter-the distance across the circle through the center, or twice the radius*

*~circumference-the distance around the circle*

*~pi-the quotient of a circles circumference and its diameter*

*(3.14159)*

## Finding the Area of a Circle

*A=πr2 Write the formula for the area of a circle*

* = 3.14(5)2(squared) Substitute 3.14 for π and 5 for r (only use 3.14 when it says to)*

* =78.5 evaluate using a calculator*

*{Area is 78.5 square inches}*

## Real Life Examples

## 10.3

**Vocabulary:***~solid-a three-dimensional figure that encloses a part of a space*

*~polyhedron-a solid that is enclosed by polygons*

*~face-the polygons that form a polyhedron*

*~prism- a polyhedron. Have 2 congruent bases that lie in parallel planes, other faces are rectangles.*

*~pyramid- a polyhedron. Pyramids have one base. The other faces are triangles*

*~cylinder-a solid with two congruent circular bases that lie in parallel planes*

*~cone-a solid with one circular base*

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

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

*~vertex-a point where three or more edges meet*

## Classifying Three-Dimensional Figures

**Polyhedron**-a solid that is enclosed by polygons

## Chart

## 10.4

**Vocabulary:***~net- a two-dimensional pattern that forms a solid when it is folded*

*~surface area-(of a polyhedron)the sum of the areas of its faces*

## Finding the Surface Area of Prisms and Cylinders

**Prism:***S=2B+Ph Write formula for surface area of a prism*

* =2(1/2*10*12)+(13+13+10)*15 Input the values for the variables*

* =660 Solve*

*{660 square centimeters}*

**Cylinder:**

*S=2πr2 +2πrh Write formula for surface area*

* =2**π(4)2(**squared)+2**π(4)*(10.7) Substitute 4 for r and 10.7 for h*

* =369.45 Evaluate using a calculator*

*{surface area is 369.45 square centimeters}*

## Real Life Examples

## 10.5

**Vocabulary:***~slant height-(l of a regular pyramid) the height of a lateral face, that is, any face that is not the base*

## Finding the Surface Area of Pyramids and Cones

**Pyramid:**

*S=B+1/2Pl Write formula for surface area of a Pyramid*

* =27.7+1/2*(24)*(6) Substitute 27.7 for B, 24 for P, and 6 for l*

* =99.7 Simplify*

*{Surface area of a pyramid is 99.7}*

**Cones:**

*S=πr2 +πrl Write Formula for surface area of a cone*

* =**π(4)2 +**π(4)*(9) Substitute 4 for r and 9 for l*

* =163.3 Evaluate using a calculator*

*{ surface area is 163.4 square meters}*

## Real Life Examples

## 10.6

**Vocabulary:**

~volume-a measure of the amount of space a solid occupies

## Finding the Volume of Prisms and Cylinder

**Prism:****Rectangle-**

*V=Bh Write formula for the volume of prism*

* =(l*w)*h write the formula for the area of the base*

* =12*(8)*(2) input the values for the variables*

* =192 Evaluate*

*{192 cubic inches}*

**Triangle-**

*V=Bh write formula for volume of a prism*

* =1/2*(4)*(3)*(10) write the formula for the area of a prism and input the values of the variables*

* =60 solve*

*{60 cubic meter}*

**Cylinder:**

*V=Bh write the formula for volume*

* =πr2h write formula for volume of a cylinder*

* =**π*(3)2(squared)*(9) substitute 3 for and 9 for h*

* =81**π simplify*

* =254.469 Evaluate with a calculator*

*{254.469 cubic centimeters}*

## Real Life Examples

## 10.7

**Vocabulary:***~pyramid- 10.3*

*~cone- 10.3*

*~volume-10.6*

## Finding the Volume of Pyramids and Cones

**Pyramid:***V=1/3Bh Write formula for volume of a pyramid*

* =1/3 *(30 squared)*(14) Substitute 30 squared for b and 15 for h*

* =4500 Evaluate *

*{4500 cubic feet}*

**Cone:**

*V=Bh write formula for volume *

* =1/3πr2h write formula for volume of a cone*

* =1/3**π*(6)squared*(12)*

* =144**π simplify*

* =452.389 Evaluate*

*{About 452 cubic feet}*

## Real Life Examples

## Finding the Volume and Surface Area for a Sphere

## Formulas

**Area of a parallelogram**- A=bh**Area of a trapezoid**- A=1/2(b1+b2)h: b1 and b2 are the 2 bases of the trapezoid

**Area of a circle**-A=πr2( pie r-squared)

**Surface area of a prism**- S=2B+Ph(B is area of the base and P is the perimeter)

**Surface area of a cylinder**-S=2B+Ch=2πr2(r-squared) +2πrh (C= circumference of the base)

**Surface Area of a Pyramid**-S=B+1/2Pl

**Volume of a Prism**-V=Bh

**Volume of a Cylinder**-V=Bh *=πr2(r-squared)h*

**Volume of a Pyramid**-V=1/3Bh

**Volume of a Cone**-V=1/3Bh=1/3πr2(r-squared)h

**Volume of a Sphere**-V=4/3πr3(r-cubed)