Prentice Hall Algebra 1

Chapter 2 Solving Equations > 2-5 Literal Equations and Formulas > Concept Byte: Finding Perimeter, Area, and Volume

Concept Byte: Finding Perimeter, Area, and Volume

Use With Lesson 2-5

You can use formulas to find the perimeters and areas of shapes called composite figures. Composite figures are composed of two or more simpler shapes.

Example 1

The composite figure below is made up of a rectangle and half of a circle. What are the perimeter and area of the figure? Use 3.14 for π.

A rectangle that is 8 centimeters long and 6 centimeters wide has a half-circle attached to 1 end. The radius of the half-circle is 3 centimeters.

Step 1 The perimeter P is the sum of the lengths of the exterior sides of the rectangle, plus half the circumference of the circle. To find the perimeter, add these measures.

P = 8 + 6 + 8 + ( 1 2 ⋅ 2 π ( 3 ) ) ≈ 8 + 6 + 8 + ( 1 2 ⋅ 2 ( 3.14 ) ( 3 ) ) = 31.42 cm table with 3 rows and 2 columns , row1 column 1 , p , column 2 equals 8 plus 6 plus 8 plus . open . 1 half , dot 2 pi , open 3 close . close , row2 column 1 , , column 2 almost equal to 8 plus 6 plus 8 plus . open . 1 half , dot 2 . open , 3.14 , close . open 3 close . close , row3 column 1 , , column 2 equals , 31.42 , cm , end table

Step 2 The total area A is the sum of the area eh sub r of the rectangle and the area eh sub h of the half circle. Use the appropriate formula to find the area of each shape. Then add to find the total area.

A r = ℓ w = 6 · 8 = 48 cm 2 table with 3 rows and 2 columns , row1 column 1 , eh sub r , column 2 equals script l w , row2 column 1 , , column 2 equals 6 middle dot 8 , row3 column 1 , , column 2 equals 48 , cm squared , end table

A h = 1 2 π r 2 ≈ 1 2 ( 3.14 ) ( 3 ) 2 = 14.13 cm 2 table with 3 rows and 2 columns , row1 column 1 , eh sub h , column 2 equals , 1 half , pi , r squared , row2 column 1 , , column 2 almost equal to , 1 half , open , 3.14 , close . open 3 close squared , row3 column 1 , , column 2 equals , 14.13 . cm squared , end table

A = A r + A h = 48 + 14.13 = 62.13 cm 2 eh equals , eh sub r , plus , eh sub h , equals 48 plus , 14.13 , equals , 62.13 . cm squared

The perimeter is 31.42 cm. The area is 61.13 . cm squared , .

A rectangular prism with length ℓ, width w, and height h and a cylinder with radius r and height h are shown below.

A rectangular prism has a length of l, a width of w, and a height of h. A right circular cylinder has a base radius of r and a height of h.

For each figure, the surface area S.A. is the sum of the area of the two bases and the lateral area.

Prism: S.A. = area of bases + lateral area

= 2ℓw + 2ℓh + 2wh

Cylinder: S.A. = area of bases + lateral area

= 2 π r 2 + 2 π r h equals 2 pi , r squared , plus 2 pi r h

The volume V of each figure is the area of the base times the height.

Prism: v equals . area of base . times , height

= ℓwh

Cylinder: v equals . area of base . times , height

equals pi , r squared , h

End ofPage 115

Concept Byte: Finding Perimeter, Area, and Volume

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