1. Lesson 8.2
Other Polygons pp

2. Objectives:
1. To define and prove formulas for the area of triangles and special quadrilaterals.
2. To apply the formulas to calculate areas of regions enclosed by them.

3. Theorem 8.2
The area of a right triangle is one-half the product of the lengths of the legs.

4. Theorem 8.3
The area of a parallelogram is the product of the base and the altitude: A = bh.

5. EXAMPLE 1 What is the area of the parallelogram?D
10″ B C
25″
A = bh
A = (25)(10)
A = 250 sq. in.

6. Theorem 8.4
The area of a triangle is one-half the base times the height: A = ½bh.

7. EXAMPLE 2 Find the area of XYZ.1 2
A = bh 9′ 1 2
A = (12)(9)
A = 54 sq. ft. Y Z
12′

8. Theorem 8.5
The area of a trapezoid is one-half the product of the altitude and the sum of the lengths of the bases:
A = ½h(b1 + b2).

9. EXAMPLE 3 Find the area of trapezoid ABCD.
18 mm
7 mm
10 mm 1 2
A = h(b1 + b2) 1 2
A = (7)( ) 1 2
A = (7)(28)
A = 98 sq. mm

10. EXAMPLE 4 Find the area of rhombus FGHI.3
A = bh
A = 4(3)
A = 12 sq. units

11. Theorem 8.6
The area of a rhombus is one-half the product of the lengths of the diagonals: A = ½d1d2.

12. EXAMPLE 5 Find the area of rhombus PQRS.4 6 1 2
A = d1d2 1 2
A = (12)(8)
A = 48 sq. units

13. Two sides of a tract of land are parallel and measure 20 km and 30 km
Two sides of a tract of land are parallel and measure 20 km and 30 km. How wide is the property between these parallel sides if the area is 850 km2?
850 = ½h(20+30)
A = ½h(b1+b2)
850 = 25h
34 = h
34 km

14. Homework pp

15. ►A. Exercises Figure Formula 1. Rectangle 2. Square 3. Triangle
Make a summary table for the area formulas learned thus far.
Figure Formula
1. Rectangle
2. Square
3. Triangle
4. Parallelogram
5. Trapezoid
6. Rhombus
A = bh
A = s2
A = ½bh
A = ½h(b1 + b2)
A = ½d1d2

16. ►A. Exercises
Find the area of each figure. 9. 4 3½

17. ►A. Exercises
Find the area of each figure.
11. 12 22 9

18. 13. A parallelogram with base 12 and height 6
►B. Exercises
Find the area of the following:
13. A parallelogram with base 12 and height 6

19. ►B. Exercises
17. Show how the formula for the area of a parallelogram can be obtained from the formula for the area of a trapezoid.

20. ►B. Exercises
23. The base of a parallelogram is three more than the height. The area is 22/9 square inches. Find the height.

21. 26. Octagon with two nonintersecting diagonals
■ Cumulative Review
Sketch an example of each.
26. Octagon with two nonintersecting diagonals

22. 27. Octahedron with vertices labeled
■ Cumulative Review
Sketch an example of each.
27. Octahedron with vertices labeled

23. 28. Closed curve that is not simple
■ Cumulative Review
Sketch an example of each.
28. Closed curve that is not simple

24. 29. Hexahedron that is a pyramid and has a concave base
■ Cumulative Review
Sketch an example of each.
29. Hexahedron that is a pyramid and has a concave base

25. 30. Sphere with three radii, each perpendicular to the other two
■ Cumulative Review
Sketch an example of each.
30. Sphere with three radii, each perpendicular to the other two