8.2: Areas of Triangles, Trapezoids, and Kites 8.4: Areas of Regular Polygons 8.3: Area Problems

congruent supplementary

rhombus

S

S

A

N

h

b

b1 b2

b2 b1

h

d1

d2 𝑨 =

𝟏

𝟐 𝒅𝟏 𝒅𝟐,

where 𝒅𝟏 𝐚𝐧𝐝 𝒅𝟐 are the lengths of the diagonals

8.4:

What is the area of one isosceles triangle in terms of a and s?

What is the area of a regular polygon in terms of a and s?

The area of a regular polygon is given by:

a s

Where a is the length of the apothem, s is the length of a side, n is the number of sides, and P is the perimeter of the polygon.

Exercises:

1) Area Rectangle GHJK A = b h A = (30) (15) A = 450 𝒄𝒎𝟐 2) Area Triangle HIJ

A = 𝟏

𝟐 b h

A = 𝟏

𝟐 (9)(12)

A = 54 𝒄𝒎𝟐

3) Area Pentagon GHIJK Area rectangle + Area Triangle 450 𝒄𝒎𝟐 + 54 𝒄𝒎𝟐 = 504 𝒄𝒎𝟐

𝑨 =𝟏

𝟐 𝒅𝟏 𝒅𝟐

𝑨 =𝟏

𝟐 𝟒𝟎 𝟕𝟎

𝑨 = 𝟏𝟒𝟎𝟎

𝒇𝒕𝟐

6 ( 1400) = 8400

𝟖𝟒𝟎𝟎

𝟒𝟎𝟎= 21

Harold should buy 21 gallons of sealant.

𝑨 =𝟏

𝟐 𝟏𝟐 + 𝟐𝟎 𝟕

𝑨 = 𝟏𝟏𝟐 𝒇𝒕𝟐

Area of the entire flowerbed 3 ( 112) = 336 𝒇𝒕𝟐

Cost =$ 100+5(336)= $ 1780

20

16.6

Area of one triangle

A= 𝟏

𝟐 b h

A= 𝟏

𝟐 (16.6)( 20)

A = 166 𝒄𝒎𝟐 Area of shaded region 6 triangles A= (6) (166) A= 996 𝒄𝒎𝟐

1) Larger hexagon, find length of one side (s) Since the figure is a regular hexagon, it is made of regular triangles, so all sides are congruent.

16 s

3) Smaller hexagon, Find length of one side (s) Since the figure is a regular hexagon, it is made of regular triangles, so all sides are congruent.

Area of shaded region≈ 662.4 – 16𝟓. 𝟔 ≈ 𝟒𝟗𝟔. 𝟖 𝒄𝒎𝟐

A= 𝟏

𝟐 a s n

2) Area of larger hexagon

A= 𝟏

𝟐 a s n

A= 𝟏

𝟐 (13.8) (16) (6)

A ≈ 662.4 𝒄𝒎𝟐

4) Area of smaller hexagon

A= 𝟏

𝟐 a s n

A= 𝟏

𝟐 (6.9) (8) (6)

A ≈ 1𝟔𝟓. 𝟔 𝒄𝒎𝟐

Homework: Workbook 8.2: All, 8.3: All, & 8.4: 1-4 & 7

Gizmos: Due 1/26 & 1/27 1. Classifying Quadrilaterals 2. Special parallelograms