unit 10-day 3 rectangles: objective: finding the perimeter & area of a rectangle
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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