LESSON 9.1

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