# Chapter 10

### Loukia A.

## Section 10.1 : Areas of Parallelograms and Trapezoids

Vocab Words...

- Base of a Parallelogram- The length of any of the parallelogram's sides.
- Height of a Parallelogram- The perpendicular distance between the base and the opposite side on a parallelogram.
- Base of a Trapezoid- One of the two parallel sides on a trapezoid.
- Height of a Trapezoid- The perpendicular distance between the bases on a trapezoid.

Key Concepts...

Area of a Parallelogram: A= b*h

Area of a Trapezoid: A= (1/2) * (b1*b2) *h

****A=area, b= base, h= height, b1 and b2= either one of the bases.

## Practice Questions

Parallelograms...

- A= 23*42
- 20= (1/2) *h

Trapezoids...

- A= (1/2) * (4 + 8) *3
- A= (1/2) * (6 + 16) *5

__Answers__

*1. A=966 units²*

*2. H= 40 units²*

*1. A= 18 units²*

*2. A= 55 units²*

## Real Life Examples

## 10.2: Area of Circles

## Vocab Words...

- Area- The amount of surface the figure covers.
- Circle- 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 though the center, or twice the radius.
- Diameter- The distance across the circle through the center, or twice the radius.
- Circumference- The distance around a circle.
- Pi (π)- An non-terminating number that for every circle, the quotient of its circumference and its diameter are the same.

## Practice Questions

Find the area of the circle given its radius (r) or diameter (d). Use 3.14 for π.

- r= 18 mi
- d= 80 in.
- d=11mm
- r= 2.9 ft.

__Answers__

*1,017.36 mi²**5,024 in.²**94.985 mm²**26.4074 ft.²*

## 10.3: Three-Dimensional Figures

## Vocab Words...

- 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 that has two congruent bases that lie in parallel planes. The other faces are rectangles.
- Pyramid- A polyhedron with one base and 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 is a solid formed by all points in space that are the same distance from a fixed point called the center.
- Edge- The segments where faces of a polyhedron meet.
- Vertex- A points where three or more edges meet.

## Practice Questions

- How many faces,edges, and vertices does a hexagonal pyramid have?
- Show two ways to represent a cylinder. Tell whether it is a polyhedron.

__Answers__

*7, 12, 7.**Answers may vary*

## Real Life Examples

## 10.4: Surface Areas of Prisms and Cylinders

## Vocab Words...

- Net- A two-dimensional pattern that forms a solid when it is folded.
- Surface Area- The sum of all the faces areas on a polyhedron.

## Key Concepts...

Surface Area of a Cylinder: S= 2B+Ch (or) 2πr²+ 2πrh

****S=Surface Area, B=Base's Area, P= Base's Perimeter, h= height

## Practice Questions

__Answers__

*2,352 cm²**72 ft²**533.8 cm²*

## Real Life Examples

## 10.5: Surface Areas of Pyramids and Cones

## Vocab Words...

- Slant Height- (represented as l in equations) The height of a lateral face, any face that is not the base.

## Key Concepts...

Surface Area of a Cone: S= πr*²+*πrl

**** S= Surface Area, B= Base's Area,

## Practice Questions

Find the surface area of the solid. Round to the nearest tenth.

- A square pyramid with a base side length 12 m and slant height 9 m.
- A cone with a radius 8 cm and slant height of 9 cm.
- A cone with the diameter 15 m and slant height 8.2 m.

__Answers__

*282 m²**427.3 cm**²**239.7 m**²*

## Real Life Examples

## 10.6: Volumes of Prisms and Cylinders

## Vocab Words...

- Volume- The measurement in the amount of space a solid occupies.

## Practice Questions

Find the volume of the solids using the exercise from 10.4. Use 3.14 for π.

- Problem 1, the rectangular prism.
- Problem 2, the triangular prism.
- Problem 3, the cylinder.

Answers

- 960 cm³
- 42 ft³
- 942 cm³

## Real Life Examples

## 10.7: Volumes of Pyramids and Cones

## Vocab Words...

- Pyramid- A polyhedron that has one base and all other faces are triangles.
- Cone- A solid with one circular base.
- Volume- The measurement in an amount of space a solid occupies.

## Key Concepts

Volume of a Pyramid: V= 1/3 Bh

Volume of a Cone: V= 1/3 Bh or V= 1/3 πr² h

**** V= volume, B= Base's area, h=height, r= radius

## Practice Questions

Find the volume of the solid. Round to the nearest tenth.

- A square pyramid with base side length of 10 ft. and height of 8 ft.
- A cone with a radius 18m and height of 6m.
- A triangular pyramid with the base side length of 9 cm and 12 cm, and a height of 14 cm.

__Answers__

*266.7 ft.³**2035.8 m³**252 cm³*

## Real Life Examples

## Spheres...

Volume of a Sphere: V= (4/3)*π*r³

Surface Area of a Sphere: 4*π*r²

Area of a Sphere: 4*π*r²