6.7 Areas of Triangles and Quadrilaterals

1
6.7 Areas of Triangles and Quadrilaterals

• Day 7

2
Warmup

• 1.
• 2.
• 3.

3
Area Postulates

• Area of a Square Postulate
• The area of a square is the square of the length
  of its sides, or A s2.
• Area Congruence 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 areas of
  its non-overlapping parts.

4
Area

• Rectangle A bh
• Parallelogram A bh
• Triangle A ½ bh
• Trapezoid A ½ h(b1b2)
• Kite A ½ d1 d2
• Rhombus A ½ d1 d2

5

• Find the area of ? ABC.

C
7
6
4
L
B
A
5
6

• Find the area of a trapezoid with vertices at
  A(0,0), B(2,4), C(6,4), and D(9,0).

7
Find the area of the figures.
4
L
L
L
L
4
4
2
L
L
L
L
4
5
8
12
8
Find the area of ABCD.
B
C
ABCD is a parallelogram Area bh
(16)(9) 144
9
E
16
A
D
12
9
Find the area of a trapezoid.

• Find the area of a trapezoid WXYZ with W(8,1),
  X(1,1), Y(2,5), and Z(5,5).

10
Find the area of rhombus.

• Find the area of rhombus ABCD.

B
Area of Rhombus A ½ d1 d2 ½ (40)(30)
½ (1200) 600
15
20
20
A
C
15
25
D
11

• The area of the kite is160.
• Find the length of BD.

A
10
B
D
C
12
Ch 6 Review

• Day 4 Part 2

13
Review 1

• A polygon with 7 sides is called a ____.
• A) nonagon
• B) dodecagon
• C) heptagon
• D) hexagon
• E) decagon

14
Review 2

• Find mltA
• A) 65
• B) 135
• C) 100
• D) 90
• E) 105

B
A
165
C
30
65
D
15
Review 3

• Opposite angles of a parallelogram must be
  _______.
• A) complementary
• B) supplementary
• C) congruent
• D) A and C
• E) B and C

16
Review 4

• If a quadrilateral has four equal sides, then it
  must be a _______.
• A) rectangle
• B) square
• C) rhombus
• D) A and B
• E) B and C

17
Review 5

• The perimeter of a square MNOP is 72 inches, and
  NO 2x 6. What is the value of x?
• A) 15
• B) 12
• C) 6
• D) 9
• E) 18

18
Review 6

• ABCD is a trapezoid. Find the length of
  midsegment EF.
• A) 5
• B) 11
• C) 16
• D) 8
• E) 22

13
A
E
11
B
5
D
F
C
9
19
Review 7

• The quadrilateral below is most specifically a
  __________.
• A) rhombus
• B) rectangle
• C) kite
• D) parallelogram
• E) trapezoid

20
Review 8

• Find the base length of a triangle with an area
  of 52 cm2 and a height of 13cm.
• A) 8 cm
• B) 16 cm
• C) 4 cm
• D) 2 cm
• E) 26 cm

21
Review 9

• A right triangle has legs of 24 units and 18
  units. The length of the hypotenuse is ____.
• A) 15 units
• B) 30 units
• C) 45 units
• D) 15.9 units
• E) 32 units

22
Review 10

• Sketch a concave pentagon.
• Sketch a convex pentagon.

23
Review 11

• What type of quadrilateral is ABCD? Explain your
  reasoning.

D
120
A
60
C
120
Isosceles Trapezoid Isosceles AD BC Trapezoid
AB ll CD
60
B