Unit 10-Day 3 Unit 10-Day 3

Rectangles:Rectangles:Unit 10-Day 3 Unit 10-Day 3

Rectangles:Rectangles:Objective: Finding Objective: Finding the Perimeter & the Perimeter &

Area of a rectangleArea of a rectangle

Rectangles:

•Opposite sides are congruent.

•All angles are right angles.

Perimeter:

w w

l

l

P = l + w + l + w P = 2l + 2w

Formula:

Example #1: Find the perimeter of a rectangle with the side length of 12 inches and a width length of 5 inches.

5 in.

12 in.P = 2(12) +

2(5)P = 24 + 10P = 34 in.

P = 2l + 2w

EXAMPLE #2

x

x+5

The perimeter of the rectangle is 26 inches. Find x.

P = 2l + 2w

26 = 2(x+5) + 2(x)

26 = 2x + 10 + 2x26 = 4x + 10

16 = 4x

-10 -10

x = 4

AREA:

A = (length)(width)

A = l w

l

w

FormulaArea of a Rectangle:

w

l

Example #3: Find the area of the rectangle.

8 in

12 in

A = l w A = (12)(8) A = 96 in.2

EXAMPLE #4:

10

65 7

Find the area of the shaded region.

( ) (big rectangle) (small rectangle)A shaded A A

30)6)(5()(

70)10)(7()(

rectsmallA

rectbigA

2403070)( unitsshadedA

Practice #2:The area of a rectangle is 50 cm2. The length is 2x and the width is x. What is the perimeter? P = 30 cm.

Day 4: Rectangular PrismDay 4: Rectangular PrismDay 4: Rectangular PrismDay 4: Rectangular PrismSurface Area and Volume Surface Area and Volume

Rectangular Prism:

A three-dimensional figure that has 6-faces that are rectangles.

Height

Length

Width

Surface Area of a Rectangular Prism:

Formula:

S.A. = + + 2LW 2LH 2WH

Formula:SA = 2LW+2LH+2WH

lengthwidth

height

Example #1: Find the surface area of a rectangular prism with a height of 5, a length of 10, & a width of 4.

5

10

4

SA = 2LW + 2LH + 2WHSA = 2(10)(4)+2(10)

(5)+2(4)(5)SA = 80 +100 + 40SA = 220 units2

Practice #1: Find the surface area of a rectangular prism with a height of 2, a length of 15, & a width of 3.

2

15

3

SA = 2LW + 2LH + 2WHSA = 2(15)(3)+2(15)

(2)+2(3)(2)SA = 90 +60 + 12SA = 162 units2

Volume:Definition:The measure in cubic units of the interior of a solid figure; or the space enclosed by a solid figure.

•Ex. How much sand will it hold?

Volume of a Rectangular Prism:

FORMULA:

V l w h

Volume: length x width x height

Example #2: Find the volume of the rectangular prism.

155

3

Volume = l w h = (15)(5)(3)

= 225 units3

Example #3: Find the side lengths of

the rectangular prism with a volume of 512 in. 3

4x2x

x

Volume = l w h

512 = (4x)(2x)(x)

512 = 8x3

8 8 64 = x3

3 3

x = 44

16

8

Practice #2:1. Find the volume of a rectangular

prism with a length of 6, height of 4, and width of 3.

2. Find the side lengths of a rectangular prism with a volume of 1500 cm3.

2x

3x2x

x = 5l = 15h = 10w = 10

V = 72 units3