Jim Smith JCHS 3108.1.9 Expand analysis of units of measure to include area and volume. 3108.4.27...
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Jim Smith JCHS Expand analysis of units of measure to include area and v 27 Use right triangle trigonometry to find the area imeter of quadrilaterals .4.28 Derive and use the formulas for the area erimeter of a regular polygon.
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Transcript of Jim Smith JCHS 3108.1.9 Expand analysis of units of measure to include area and volume. 3108.4.27...
Jim SmithJCHS
3108.1.9 Expand analysis of units of measure to include area and volume.
3108.4.27 Use right triangle trigonometry to find the area and perimeter of quadrilaterals
3108.4.28 Derive and use the formulas for the area and perimeter of a regular polygon.
PERIMETERThere are many formulas
(or shortcuts) for finding theperimeter of polygons. The only one you need to remember is….
ADD ALL SIDESThis will work for all polygons
8
88
3 3
99
4
13
7
5
4
7
4
5
4
7
P= 3+8+3+8=22 P= 4+5+5+4+7=25
P= 9+9+4=22
P= 13+7+4+7=31
Area of RectanglesThink of filling the rectangle with boxes. All answers should be in square units.
4
3
4 ColumnsBy 3 Rows
4X3= 12This is the lengthtimes the width
A= lw
551
38
12A=lw
A=51x5A=255 sq units
A=lwA=38x12
A=456 sq units
Rectangles
Area of Parallelograms
h
b
A=bh
The height must form a right anglewith a base
7
10
15
6
A=bhA=10x7
A=70 sq. units
A=bhA=15x6
A=90 sq. units
Parallelograms
Area of Triangles
b b
h h
A=1/2 bh
Triangles
21
7
A = ½ bhA = ½ 7x21A = ½ 147
A = 147 2A = 73½A = 73.5 sq units
Right Triangle Equilateral orIsosceles Triangle
6
8
A = ½ bhA = ½ 6 x 8A = 24 Sq. Unit
10 10
1060° 60°
60°
5 5
5√3
A = ½ bhA = ½ 10 x 5√3A = 25√3 Sq. Unit
Area of Trapezoidsb1
b2
h
A = ½ h( b1 + b2 )
8
6
12A = ½ h(b1 + b2)A = ½ (6)( 8+12 )A = 3( 20 )A = 60 sq units
Trapezoid
45°
8
148 6
6
A = ½ h(b1 + b2)A = ½ 6( 8+14 )A = ½ 6(22)A = 66 sq units
Trapezoid with 45°
45°
6
60°
6
166
5 560°5√3
5
A=1/2 h( b1+b2 )A= ½ 5√3 ( 6+16 )A= ½ 5√3 ( 22 )A= 5√3 ( 11 )A= 55√3 sq units
Isosceles Trapezoid
Area of Rhombiand Kites
d1 d2
A = ½ d1 x d2
d2
d1
( d1 and d2 are the whole diagonals )
Rhombus and Kite
108X6
8 6
A = ½ d1 x d2
A = ½ 12x16A = 96 sq units
43 7
4
A = ½ d1 x d2
A = ½ 8x10A = 40 sq units
Area of Regular Polygons
s
r
a
s = sidea = apothemr = radius
A=1/2 aP
6
5
3 3
4 3²+x² = 5²
A = ½ aPA = ½ 4x36A = 72 sq units
P = 6x6P = 36
Regular Hexagon
The area of any figure is the sum of all the non-overlapping parts
Trapezoid
Triangle
Rectangle
+ + +Add The Parts
OR
Complete the figure and subtract thepart you don’t want ( bake the cakeand eat the part you don’t want! )
