6.7 Areas of Triangles and Quadrilaterals. The area of a Square Area of a Square.

6.7 Areas of 6.7 Areas of Triangles and Triangles and

Quadrilaterals Quadrilaterals

The area of a Square

Area of a Square

X

X

X

X

2xA

Postulate

If two polygons are congruent, then they have the same area.

Area Addition Postulate

The area of a region is the sum of the area of it nonoverlapping parts.

The Blue area is Area of

A+B+C+D+E+F+G+H

The Area of a Rectangle

Area of a Rectangle is Base times height.

base

height

The Area of a Parallelogram

Area of a Parallelogram

is Base times height.

base

height

Area of a Triangle

Area is one half base times height, even if the height is outside of the triangle

height

base

Area of a Trapezoid

Area is one half height times(base1 + base2).

Height is from base1 to base2

Area of a Kite

Area is one half of diagonal1times

diagonal2

Area of a Rhombus

Area is one half of diagonal1 times

diagonal2

Find the Area

Square

4.15ofside

Find the Area

Square Area 237.16 in2

inofside 4.15

Find the Area

Rectangles Area =

inofside 1.4inofside 2.7

inofside 8.3

inofside 5.1

Find the Area

Rectangles Area = 27.36in2 + 6.15in2 = 33.51 in2

inofside 1.4inofside 2.7

inofside 8.3

inofside 5.1

Find the Area

Parallelogram Area =

inofheight 7.3

inofbase 4.16

Find the Area

Parallelogram Area = 60.68 in2

inofheight 7.3

inofbase 4.16

Find the Area

Find the area of the Trapezoid

3,2

1,2

4,2

2,2

Find the Area

Find the area of the Trapezoid

height = 4

base1 = 4

base2 = 6

3,2

1,2

4,2

2,2

41631)2(2 22

Find the Area

Find the area of the Trapezoid

Area height = 4

½(4)(4+6)

½(4)(10) base1 = 4

2(10) base2 = 6

Area = 20

3,2

1,2

4,2

2,2

41631)2(2 22

Find the length of the diagonal

Rhombus Area is 192 units2

8 16

Find the length of the diagonal

Rhombus Area is 192 units2

192 = ½(8+16)(diagonal)

192 = ½(24)(diagonal)

192 = 12(diagonal)

16 = diagonal

What is x ?

8 16

x

Find the Area

What is the total Area

in8 in8

in16

in10

in3

Find the Area

What is the total Area Trap = ½(3)(10+16) = 39

Rect. = 8(16) = 128

Total = 167in2

in8 in8

in16

in10

in3

Homework

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