1. Section 10A Fundamentals of Geometry
Pages

2. 10-A
Regular Polygons

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. Perimeter and Area - Summary

9. 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

10. 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

11. 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 miles×4 = 48 miles
Area = (12 miles)2 = 144 miles2 12 12

12. 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

13. 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

14. 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?

15. Surface Area and Volume

16. 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

17. 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

18. 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.

19. 10-A
Homework
Pages
# 34, 42, 46, 48, 50, 52, 56, 58, 61,84