LESSON 9.1Areas of Rectangles and Parallelograms
AREA OF A RECTANGLE
C-81: The area of a rectangle is given by the
formula A=bh. Where b is the length of the
base and h is the height.
AREA OF A PARALLELOGRAM
C-82: The area of a parallelogram is given by the formula A=bh. Where b is the length of the
base and h is the height of the
parallelogram.
LESSON 9.2Areas of Triangles, Trapezoids and Kites
AREA OF TRIANGLES
C-83: The area of a triangle is given by the formula
. Where b is the length of the base and h is the height (altitude) of the triangle.
A =bh2
AREA OF TRAPEZOIDS
C-84: The area of a trapezoid is given by the
formula . Where the b's are the length of the bases and h is
the height of the trapezoid.
A =(b1 +b2 )h
2
AREA OF KITES
C-85: The area of a kite is given by the formula . Where the d's are the length of the diagonals of
the triangle.
A =
d1gd2
2
LESSON 9.4Areas of Regular Polygons
AREA OF REG. POLYGONSA regular n-gon has "n" sides and "n" congruent triangles in its interior.The formula for area of a regular polygon is derived from theses interior congruent triangles. If you know the area of these triangles will you know the area of the polygon?
FORMULA TO FIND AREA OF A REGULAR POLYGON
A =ngbh2
A=ngas2
A=nas2
n= # of sidesa = apothem lengths = sides length
FORMULA TO FIND AREA OF A REGULAR POLYGON
C-86: The area of a regular polygon is given by
the formula , where a is the apothem (height of interior triangle), s is the length of
each side, and n is the number of sides the polygon has.
Because the length of each side times the number of sides is the perimeter, we can say
and .
A =nas2
P =sn A =aP2
LESSON 9.5Areas of Circles
AREA OF A CIRCLE
C-87: The area of a circle is given
by the formula , where A is
the area and r is the radius of the
circle.
A = 2rπ
LESSON 9.6Area of Pieces of Circles
SECTOR OF A CIRCLE
A sector of a circle is the region between two radii of a circle and the included arc.Formula:Central Angle
360=Area of Sector
2rπ
AREA OF SECTOR EXAMPLE
Find area of sector.
Central Angle360
=Area of Sector
2rπ
45
360=
x212 π
19=
x144π
144π9
=x
16π =x
SEGMENT OF A CIRCLE
A segment of a circle is the region between a chord of a circle and the included arc.Formula:
Area of Segment=Area of Sector - Area of TriangleSee Example on Next Slide
SEGMENT OF A CIRCLE EXAMPLE
Find the area of the segment.
62πg90360
⎡⎣⎢
⎤⎦⎥−
6g62
⎡⎣⎢
⎤⎦⎥
=36π14−362
=364π −18
=9π −18cm 2
ANNULUS
An annulus is the region between two concentric circles.Formula:
A =R 2π −r2π
LESSON 9.7Surface Area
TOTAL SURFACE AREA (TSA)
The surface area of a solid is the sum of the areas of all the faces or surfaces that enclose the solid.The faces include the solid's top and bottom (bases) and its remaining surfaces (lateral surfaces or surfaces).
TSA OF A RECTANGULAR PRISM
Find the area of the rectangular prism.
TSA =2(4g10)+ 2(7g4)+ 2(7g10)=80 + 56 +140
=276cm 2
TSA OF A CYLINDERFormula:
Example:
TSA =2(r2π)+ 2rπgh
TSA =2(62π)+ 2(6)πg20=2(36π)+ 240π=72π + 240π
=312πun2
TSA OF A PYRAMID The height of each triangular face is called the slant height.The slant height is usually represented by "l" (lowercase L).Example:
TSA =Base Area+ Lateral Surface Area
=25g25 + 432g252
⎛⎝⎜
⎞⎠⎟
=625 + 4(400)=625 +1600
=2225 ft2
TSA OF A CONE• Formula:
• Example:
TSA =Area of Base + Lateral Surface Area
=r2π + rπl
TSA =82π + 8π9=64π + 72π
=136πcm 2