Chapter 8: Area8.1/8.2 Area of Basic Figures

Objectives: Understand and solve the areas of parallelograms, triangles, trapezoids, and rhombi.

**What about rectangles?

**What about squares?

Find the area or missing side:

Area of a triangle:

Find the area:

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Chapter 8: Area

Find the unknown measurement of the triangle if the area is 30 ft2 and the base is 10 ft.

Area of a Trapezoid:

Find the area:

Area of a Rhombus:

Chapter 8: Area

Find the area:

8.3 The Pythagorean Theorem

Chapter 8: Area

Find the missing length in the right triangle:Legs of 8 and 15. Legs of 10 and 24. Legs of 5 and 12.

Hypotenuse 25, leg 20. Hypotenuse 7, leg 5. Hypotenuse 61, leg 60.

Given the 3 side lengths, are the following triangles right triangles?15, 36, and 39 10, 20, and 22 14, 48, and 50

8.4 Regular Polygons

Chapter 8: AreaVocabulary:Regular polygon:

Center of a regular polygon:

Radius of a regular polygon:

Apothem of a regular polygon:

Central angle of a regular polygon:

Base angle of a regular polygon:

Objectives:Define terms related to regular polygons.Derive and apply a formula for the area of regular polygons.

The central angles of a regular n-gon are congruent and measure 360°n .

What are the measures of the central angles and the base angles of a regular hexagon?

The area of a regular polygon is one-half the product of its apothem and its perimeter: A=1

2ap

The apothem of an equilateral triangle is one-third the length of the altitude: a=13 h

Find the areas:

8.5 Area of Circles

Chapter 8: Area

Find the area:

Composite figures - find the area of the shaded region

8.6 Surface Areas of Prisms and CylindersVocabulary:Surface area:

Objectives:Differentiate between surface area and lateral surface area.

Chapter 8: AreaDerive and apply formulas for calculating the surface area of prisms and cylinders.

Nets:

To calculate surface area of a prism/cylinder:Find Lateral Surface Area. Add the 2 bases to it.

Find the surface areas:

Chapter 8: Area

8.7 Surface Areas of Pyramids and ConesObjectives:Distinguish between the total surface area and the lateral surface area of pyramids and cones.Derive and apply formulas for calculating the surface area of pyramids and cones.

Pyramids: Add up the areas of the triangles and the area of the base.S=L+B L=lateral surface area, B=area of base

Find the surface area:

Chapter 8: Area

Cones: Add up the slanted side of the cone and the area of the circular base. S=πrl+π r2 r=radius, l=slant height

Find the surface area:

8.8 Surface Areas of Polyhedra and SpheresObjectives:State and apply the formula for surface area of a sphere.Name the regular polyhedra.State and apply formulas for surface areas of regular polyhedral.

Spheres: S=4 π r2

Find the surface area:

Chapter 8: Area

Regular Polyhedron: a polyhedron with faces bounded by congruent regular polygons and with the same number of faces intersecting at each vertex.

To find the surface area:S=nA n=number of faces, A=area of one face

Area of one face=5