6.7 Areas of Triangles and Quadrilaterals
Dec 25, 2015
6.7 Areas of Triangles and Quadrilaterals
Warmup
1.
2.
3.
5
12
6
5
11
2
4
3
4
1
3
1
12
11
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.
Area
Rectangle: A = bh Parallelogram: A = bh Triangle: A = ½ bh Trapezoid: A = ½ h(b1+b2)
Kite: A = ½ d1 d2
Rhombus: A = ½ d1 d2
Find the area of ∆ ABC.
A B
C
7
5
64
L
Find the area of a trapezoid with vertices at A(0,0), B(2,4), C(6,4), and D(9,0).
Find the area of the figures.
4
4
4
4
LL L
L
L
LL
L
2
5
12
8
Find the area of ABCD.
A
B C
D
E
12
16
9
ABCD is a parallelogramArea = bh = (16)(9) = 144
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).
Find the area of rhombus.
Find the area of rhombus ABCD.
A
B
C
D
20 20
15
15 25
Area of Rhombus A = ½ d1 d2
= ½ (40)(30) = ½ (1200) = 600
The area of the kite is160. Find the length of BD.
A
B
C
D10
Ch 6 Review
Day 4 Part 2
Review 1
A polygon with 7 sides is called a ____.A) nonagon
B) dodecagon
C) heptagon
D) hexagon
E) decagon
Review 2
Find m<A
A) 65°
B) 135°
C) 100°
D) 90°
E) 105°
AB
C
D
165°30°
65°
Review 3
Opposite angles of a parallelogram must be _______.
A) complementary
B) supplementary
C) congruent
D) A and C
E) B and C
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
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
Review 6
ABCD is a trapezoid. Find the length of midsegment EF.
A) 5
B) 11
C) 16
D) 8
E) 22
A
B
CD
E
F
11
5
9
13
Review 7
The quadrilateral below is most specifically a __________.
A) rhombus
B) rectangle
C) kite
D) parallelogram
E) trapezoid
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
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
Review 10
Sketch a concave pentagon.
Sketch a convex pentagon.
Review 11
What type of quadrilateral is ABCD? Explain your reasoning.
A
B
C
D
120°
120°60°
60°
Isosceles TrapezoidIsosceles : AD = BCTrapezoid : AB ll CD