1. Section 10A Fundamentals of Geometry
Pages

2. Perimeter and Area - Summary

3. Perimeter and Area Rectangles
= l+ w+ l+ w
= 2l + 2w
Area
= length × width
= l × w

4. Perimeter and Area Squares
= l+l+l+l
= 4l
Area
= length × width
= l × l
= l2

5. Perimeter and Area Triangles
= a + b + c
Area
= ½×b×h

6. Perimeter and Area Parallelograms
= l+ w+ l+ w
= 2l + 2w
Area
= length × height
= l×h

7. Perimeter and Area Circles
Circumference(perimeter)
= 2πr
= πd
Area
= πr2
π ≈ …

8. Practice with Area and Perimeter Formulas
Find the circumference/perimeter and area for each figure described:
33/589 A circle with diameter 25 centimeters
Circumference = πd = π×25 cm= 25π cm
Area = πr2 = π×(25/2 cm)2 = π cm2 25

9. Practice with Area and Perimeter Formulas
Find the circumference/perimeter and area for each figure described:
41/589 A rectangle with a length of 2 meters and a width of 8 meters
Perimeter = 2m + 2m + 8m + 8m = 20 meters
Area = 2 meters × 8 meters = 16 meters2 8 2

10. Practice with Area and Perimeter Formulas
Find the circumference/perimeter and area for each figure described:
37/589 A square with sides of length 12 miles
Perimeter = 12 km×4 = 48 miles
Area = (12 meters)2 = 144 miles2 12 12

11. Practice with Area and Perimeter Formulas
Find the circumference/perimeter and area for each figure described:
39/589 A parallelogram with sides of length 10 ft and 20 ft and a distance between the 20 ft sides of 5 ft.
Perimeter = 10ft +20 ft +10ft +20ft = 60ft
Area = 20ft × 5 ft = 100 ft2 20 10 5

12. Practice with Area and Perimeter Formulas
45/589 Find the perimeter and area of this triangle
Perimeter = = 33 units
Area = ½ ×15×4 = 30 units2 9 15 4

13. Applications of Area and Perimeter Formulas
47/589 A picture window has a length of 4 feet and a height of 3 feet, with a semicircular cap on each end (see Figure 10.20). How much metal trim is needed for the perimeter of the entire window, and how much glass is needed for the opening of the window?
49/589 Refer to Figure 10.14, showing the region to be covered with plywood under a set of stairs. Suppose that the stairs rise at a steeper angle and are 14 feet tall. What is the area of the region to be covered in that case?
51/589 A parking lot is bounded on four sides by streets, as shown in Figure How much asphalt (in square yards) is needed to pave the parking lot?

14. Surface Area and Volume

15. Practice with Surface Area and Volume Formulas
79/591 Consider a softball with a radius of approximately 2 inches and a bowling ball with a radius of approximately 6 inches. Compute the surface area and volume for both balls.
Softball: Surface Area = 4xπx(2)2 = 16π square inches Volume = (4/3)xπx(2)3 = (32/3) π cubic inches
Bowling ball: Surface Area = 4xπx(6)2 = 144π square inches Volume = (4/3)xπx(6)3 = 288 π cubic inches

16. Practice with Surface Area and Volume Formulas
ex6/585 Which holds more soup – a can with a diameter of 3 inches and height of 4 in, or a can with a diameter of 4 in and a height of 3 inches?
Volume Can 1 = πr2h
= π×(1.5 in)2×4 in = 9π in3
Volume Can 2 = πr2h
= π×(2 in)2×3 in = 12π in3

17. Practice with Surface Area and Volume Formulas
59/585 The water reservoir for a city is shaped like a rectangular prism 300 meters long, 100 meters wide, and 15 meters deep. At the end of the day, the reservoir is 70% full. How much water must be added overnight to fill the reservoir?
Volume of reservoir = 300 x 100 x 15 = cubic meters
30% of volume of reservoir has evaporated.
.30 x = cubic meters have evaporated.
cubic meters must be added overnight.

18. 10-A
Homework
Pages
# 34, 52, 58, 61, 84

19. Section 10B Problem Solving with Geometry pages 597-608

20. Pythagorean Theorem c a2 + b2 = c2 a b
For a right triangle with sides of length a, b, and c in which c is the longest side (or hypotenuse), the Pythagorean theorem states: a b c
a2 + b2 = c2

21. Pythagorean Theorem
example If a right triangle has two sides of lengths 9 in and 12 in, what is the length of the hypotenuse?
(9 in)2+(12 in)2 = c2
81 in2+144 in2 = c2
225 in2= c2 c 9 12

22. Pythagorean Theorem
example If a right triangle has a hypotenuse of length 10 cm and a short side of length 6 cm, how long is the other side?
(6)2 + b2 = (10)2
36 + b2 = 100
b2 = (100-36) = 64 10 6 b

23. Pythagorean Theorem
ex5/597 Consider the map in Figure 10.30, showing several city streets in a rectangular grid. The individual city blocks are 1/8 of a mile in the east-west direction and 1/16 of a mile in the north-south direction.
How far is the library from the subway along the path shown?
How far is the library from the subway “as the crow flies” (along a straight diagonal path)?
subway
library

24. Similar Triangles
Two triangles are similar if they have the same shape (but not necessarily the same size), meaning that one is a scaled-up or scaled-down version of the other.
For two similar triangles:
corresponding pairs of angles in each triangle are equal. Angle A = Angle A’, Angle B = Angle B’, Angle C = Angle C’
the ratios of the side lengths in the two triangles are all equal a’ b’ c’ A’ B’ C’ B a b A C c

25. Similar Triangles 67/605 Complete the triangles shown below. 50 x y 1040

26. Homework
Pages
#52,66,84,86,88