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.

Area Formulas

Chapter 10.1

A Rectangle = b * h A 𝑃𝑎𝑟𝑎𝑙𝑙𝑒𝑙𝑜𝑔𝑟𝑎𝑚 = b * h A 𝑇riangle = 1 2 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 10.2

Area Formulas A 𝑇𝑟𝑎𝑝𝑒𝑧𝑜𝑖𝑑 = 1 2 ℎ (𝑏 1 + 𝑏 2 ) A Rhombus or Kite = 1 2 𝑑 1 𝑑 2

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

Area Regular Polygon = 1 2 a P ( a – apothem & P – perimeter )

Steps to find the Area of a Regular Polygon 1) First find the central angle of the polygon 2) Drop an altitude down from the central angle and find the apothem by using SOH-CAH-TOA 3) Find the other leg of the triangle.

4) Find the one of the sides of the polygon 5) Find the perimeter of the polygon 6) Use the formula to find the area A = ½ a P

Area formula for a Equilateral Triangle

A =

𝟏 𝟒 𝟑 (𝑺𝒊𝒅𝒆) 𝟐

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 𝑎 𝑏 (1) the ratio of their perimeter is also 𝑎 𝑏 (2) the ratio of their areas is 𝑎 2 𝑏 2 then,

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

Area of ABC = 1 2 𝑏 𝑐 (sin 𝐴) 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.

Minor arc AB Semi Circle ABC Major Arc ABD

Chapter 10.6

Circumference of a Circle – 2  r or d  Arc Length Formula – mAB * 2  r 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  r 2 Area of a Sector mAB *  r 2 360°

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 – 𝑃𝑜𝑠𝑠𝑖𝑏𝑙𝑒 𝐴𝑟𝑒𝑎 𝑇𝑜𝑡𝑎𝑙 𝐴𝑟𝑒𝑎 Probability is usually written as a percent.