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
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
Hexagonal Prism
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.