Chapter 10.1

Common Core G.MG.1 & G.GPE.7 – Use geometric shapes, their measures, and their properties to describe objects. Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

Objective – To find the area of parallelograms and triangles.

Chapter 10.1Area Formulas

= b * h

= b * h

= b * h

Chapter 10.2

Common Core G.MG.1 – Use geometric shapes, their measures, and their properties to describe objects.

Objective – To find the area of a trapezoid, rhombus, or kite.

Chapter 10.2Area Formulas

=

=

Chapter 10.3

Common Core G.MG.1 – Use geometric shapes, their measures, and their properties to describe objects.

Objective – To find the area of a regular polygon.

Chapter 10.3=

(a – apothem & P – perimeter)

Steps to find the Area of a Regular Polygon

1) First find the central angle of the polygon2) Drop an altitude down from the central angle

and find the apothem by using SOH-CAH-TOA3) Find the other leg of the triangle.4) Find the one of the sides of the polygon5) Find the perimeter of the polygon6) Use the formula to find the area A = ½ a P

Area formula for a Equilateral TriangleA =

Chapter 10.4

Common Core G.GMD.3 – Use volume formulas for cylinders, pyramids, cones, and sphere to solve problems.

Objective – To find the perimeters and areas of similar polygons.

Chapter 10.4

Perimeters and Areas of Similar Figures

If the scale factor of two similar figures is then,(1) the ratio of their perimeter is also (2) the ratio of their areas is

Chapter 10.5

Common Core G.SRT.9 – Derive the formula A = ½ ab sin(C) for the are of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.

Objective – To find areas of regular polygons and triangles using trigonometry.

Chapter 10.5

ABC

B c a

A C b

Chapter 10.6

Common Core G.CO.1, G.C.1, G.C.2 & G.C.5 – Know precise definitions of…circle…Prove that all circles are similar.

Objectives – To find the measures of central angles and arcs. To find the circumference and arc length.

Chapter 10.6

Minor arc AB Semi Circle ABCMajor Arc ABD

Circumference of a Circle – 2r or d

Arc Length Formula – mAB * 2r

360°

Chapter 10.7

Common Core G.C.5 – Derive using similarity the fact that the length of the are intercepted by an bale is proportional to the radius, and derive the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Objective – To find the areas of circles, sectors, and segments of circles.

Chapter 10.7 Notes

Area of a Circle - r2

Area of a Sector - mAB * r2

360°

Area of a Segment – take the area of the sector and subtract the area of the triangle

= -

Chapter 10.8

Common Core S.CP.1 – Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections, or complements of other events.

Objective – To use segment and area models to find the probabilities of events

Chapter 10.8 Notes

Geometric Probability –

Probability is usually written as a percent.