# daily warm-up quiz 1.write the distance formula: d = ___________________ 2. write the slope formula:...

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Daily Warm-UP Quiz 1.Write the distance formula: d = ___________________ 2. Write the slope formula: 3. Given: A (-5,2) B (-3,6) Find a. The slope of AB Find b. The length of AB Mrs. McConaughy Geometry 1

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1. Write the distance formula: d = ___________________2. Write the slope formula:3. Given: A (-5,2) B (-3,6)Find a. The slope of AB Find b. The length of AB

Mrs. McConaughy Geometry 1 Mrs. McConaughy Geometry 2

Lesson 7.1: Areas of Triangles and Quadrilaterals

Objective: To find the areas of squares, rectangles, parallelograms, and triangles Mrs. McConaughy Geometry 3

AREA POSTULATES

AREA OF A SQUARE POSTULATEThe area of a square is ___________________________________________.AREA CONGRUENCE POSTULATEIf two polygons are congruent, _____________________________________.AREA ADDITION POSTULATEThe area of a region is ___________________________________________.

A = s2, where s is the length of its side.

then they have the same area.

the sum of the areas of its non-overlapping parts. Mrs. McConaughy Geometry 4

AREA THEOREMS

A = ½ bh *

Area = bh

Area of a TriangleThe area of a parallelogram is one half the product of a base and its corresponding height* (where h is the altitude).

Area of a Rectangle (or Square)*The area of a rectangle (or square) is the product of its base and height.

Area of a ParallelogramThe area of a parallelogram is the product of a base and its corresponding height* (where height is the altitude).

Area = bh*

NOTE: Area is always measured in square units.

b

h

b

h

b

h Mrs. McConaughy Geometry 5

Using Area Theorems: Parallelograms

A base of a parallelogram is _______________________________.

The height of a parallelogram corresponding to a given base is ______________________________________________________________.

any of its sides

the perpendicular segment to the line containing the base (altitude) . Mrs. McConaughy Geometry 6

Find the area of ABCD.

Area = bh

Area = (16) (9)

Area = 144 units2

OR

Area = bh

Area = (12) (12)Area = 144 units2

Note: You get the same area with either base.

Remember: Area is always measured in square units. Mrs. McConaughy Geometry 7

Finding a Missing Dimension

Given: Area = 126 cm2 h = 14 cm b = ___________ Mrs. McConaughy Geometry 8

Finding a Missing Dimension

A parallelogram has sides of 15 cm and 18 cm. The height corresponding to a 15-cm base is 9 cm. Draw the parallelogram and find the height corresponding to an 18-cm base. 15 cm

18 cm

9 cm Mrs. McConaughy Geometry 9

Work Space:

Area = bh = ______ = ______

Area = bh

____ = _____

____= _____Remember: Area is always measured in square units. Mrs. McConaughy Geometry 10

Using Area Theorems: Triangles

A base of a triangle is _____________________________.

The height of a triangle is __________________________________________________________.

any of its sides

the length of the altitude to the line containing that base Mrs. McConaughy Geometry 11

Identifying the base and height in triangles. Mrs. McConaughy Geometry 12

Using Areas: Triangle Areas

Find the area of the TRIANGLE at the left. Area = _________ Area = _________ Area = _________

½ bh

½ (12m) (15 m)90 m2

Remember: Area is always measured in square units. Mrs. McConaughy Geometry 13

Structural Design

The front of a garage is a square 15 ft. on each side with a triangular roof above the square. The height of the triangular roof is 10.6 ft. To the nearest hundredth, how much force is exerted by an 80 mi/h wind blowing directly against the front of the garage? Use the formula, F = 0.004 Av2, where F is the force in pounds, A is the surface area in square feet, and v is the velocity of the wind in mph. Mrs. McConaughy Geometry 14

FINAL CHECKS FOR UNDERSTANDING

1. If you use AB as the base to find the area of parallelogram ABCD shown at the right, what should you use as the height?

2. Find the area of the polygon.

HOMEWORK: _______________________