Trapezoids, and Kites 8.4: Areas of Regular …...2014/08/16 · 8.4: Areas of Regular Polygons...
Transcript of Trapezoids, and Kites 8.4: Areas of Regular …...2014/08/16 · 8.4: Areas of Regular Polygons...
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