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