# Chapter 10

## ALL FORMULAS FOR AREA

Circle- Pi(R^2)

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

Cone- Pi(R^2)+Pi(R)(l)

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

Parallelogram Formula- b(h) {b stands for base h for height}

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.

## 10.2 Areas of Circles

Circle Area Formula- Pi(R^2) {Check test for 3.14 or Pi R stands for radius of circle, square that.

## 10.2 Vocabulary

Area: The amount of surface the figure covers.

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.

## 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)

Net:A two dimensional pattern that creates a 3 dimensional object when folded together.

Surface Area: The sum of all areas.

## 10.5 Vocabulary Surface Area of Pyramid and Cone

Slant Height-The height of the lateral base going down the middle.

For surface area formulas see part 2.

## 10.6 Volumes of Prisms and Cylinders

Volume- The amount of space a object occupies.

For volume formulas see volume part.

## 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.

## 10.7 Real life Example

Volume of Hexagonal Prism - GeRometry