# Chapter 10

### Brandon W.

## ALL FORMULAS FOR AREA

Rectangle-B(h)

Parallelogram- B(h)

Cone- 1/3 (Pi)(R^2)h

Trapezoid- .5(b1+b2)h

Triangle- .5b(h)

Cylinder-B(h)

Pentagon- Use Trigonometry (10 Triangles) [36 Top 54 Lower] Triangle formula(5)

Hexagon- (3(square root 3)(s^2))/2

Heptagon- Use trig to divide it into 14 triangles then [64.285](14)

## ALL FORMULAS FOR SURFACE AREA

Cylinder- 2(Pi)(R^2)+2(Pi)(R)(h)

Sphere- 4(Pi)(R^2)

Cube- 6(S^2)

Rectangular Prism- 2(lw+wh+lh)

Pentagonal Prism- B(Pentagon)+H(Area of rectangle(5) Add them

Hexagonal Prism- B(Hexagon)+H(Area of Rectangle(6) Add them

Heptagonal Prism- B(Heptagon)+(Area of Rectangle(7) Add them

Any Pyramid- B+1/2pl

## 10.1 Areas of Trapezoids and Parallelogram's

Trapezoid Formula- 1/2(b1+b2)h {b1 is top base b2 bottom base}

## 10.1 Vocabulary

- Base of Parallelogram: Is the length of any of its sides.
- Height of Parallelogram: The perpendicular distance between the base and the opposite side (not on side in the inside of shape.)
- Bases of Trapezoid: Its two parallel sides.
- Height of Trapezoid: The perpendicular distance between its bases.

## 10.1 Real life Example

## 10.2 Areas of Circles

## 10.2 Vocabulary

Radius: The distance from the center to any outer edge.

Diameter: The distance from edge to edge passing through the center.

Circumference: Distance around the circle.

## 10.2 Real Life Example

## 10.3 Three Dimensional Figures

## Shape names (Left to Right Up to Down) 10.3 1. Cone- Area-Part 1, Surface Area- Part 2 2. Cylinder-Area-Part 1, surface Area-Part 2 3. Sphere- Area-Part 1, Surface Area-Part 2 4. Cube-Surface Area-Part 2 5. Triangular Prism- 6. Triangular Pyramid 7. Rectangular Prism 8. Hexagonal Prism 9. rectangular Pyramid | ## Three Dimensional Figures All Formulas on Part 1 Or Part 2 | ## Hexagonal Prism |

## Shape names (Left to Right Up to Down) 10.3

2. Cylinder-Area-Part 1, surface Area-Part 2

3. Sphere- Area-Part 1, Surface Area-Part 2

4. Cube-Surface Area-Part 2

5. Triangular Prism-

6. Triangular Pyramid

7. Rectangular Prism

8. Hexagonal Prism

9. rectangular Pyramid

## 10.3 Real Life Example

## ALL FORMULAS FOR VOLUME

- Triangular Prism-B(h) {B is for Area of Base (Triangle 1/2(b)(h)(h*) Second height is from the Square/Rectangle}
- Rectangular Prism- B(h)(w)
- Pentagonal Prism- B(h)
- Hexagonal Prism- See picture
- Cylinder- Pi(R^2)h
- Pyramid- 1/3(B)(h)
- Cones- 1/3(Pi)(R^2)(h)
- Sphere- 4/3(Pi(R^3)

## 10.4 Vocabulary (Prisms and cylinders)

Surface Area: The sum of all areas.

## 10.4 Real Life Example

## 10.5 Vocabulary Surface Area of Pyramid and Cone

For surface area formulas see part 2.

## 10.5 Real Life Example

## 10.6 Volumes of Prisms and Cylinders

For volume formulas see volume part.

## 10.6 Real Life Example

## 10.7 Volumes of Pyramids and Cones

- A pyramid is a polyhedron with one base, all sides are triangles, go to one point at the top.
- A solid with one circular base.
- For formulas look in Volume part.