1. Five-Minute Check (over Chapter 9) Mathematical Practices Then/Now
New Vocabulary
Postulate 10.1: Area Addition Postulate
Key Concept: Area of a Parallelogram
Example 1: Perimeter and Area of a Parallelogram
Example 2: Area of a Parallelogram
Postulate 10.2: Area Congruence Postulate
Key Concept: Area of a Triangle
Example 3: Real-World Example: Perimeter and Area of a Triangle
Example 4: Perimeter and Area on the Coordinate Plane
Lesson Menu

2. Name a radius. A. B. C. D.
5-Minute Check 1

3. Name a chord. A. B. C. D.
5-Minute Check 2

4. A. 90
B. 120
C. 160
D. 170
5-Minute Check 4

5. Find mADC if the mACD = 42.
B. 42
C. 48
D. 84
5-Minute Check 4

6. Write an equation of the circle with center at (–3, 2) and a diameter of 6.
A. (x + 3) + (y – 2) = 9
B. (x – 3) + (y + 2) = 6
C. (x + 3)2 + (y – 2)2 = 9
D. (x – 3)2 + (y + 2)2 = 6
5-Minute Check 5

7. Which of the following figures is always perpendicular to a radius of a circle at their intersection on the circle?
A. chord
B. diameter
C. secant
D. tangent
5-Minute Check 6

8. Mathematical Practices
1 Make sense of problems and persevere in solving them.
7 Look for and make use of structure.
Content Standards
G.GPE.7 Use coordinates to compute perimeters of polygons and areas of triangles and rectangles, e.g., using the distance formula. MP

9. You found areas of rectangles and squares.
Find perimeters and areas of parallelograms.
Find perimeters and areas of triangles.
Then/Now

10. base of a parallelogram
height of a parallelogram
base of a triangle
height of a triangle
Vocabulary

11. Concept 1

12. Concept 2

13. Find the perimeter and area of
Perimeter and Area of a Parallelogram
Find the perimeter and area of
Perimeter Since opposite sides of a parallelogram are congruent, RS UT and RU ST. So UT = 32 in. and ST = 20 in.
Example 1

14. Perimeter = RS + ST + UT + RU = 32 + 20 + 32 + 20 = 104 in.
Perimeter and Area of a Parallelogram
Perimeter = RS + ST + UT + RU =
= 104 in.
Area Find the height of the parallelogram. The height forms a right triangle with points S and T with base 12 in. and hypotenuse 20 in.
c2 = a2 + b2 Pythagorean Theorem
202 = b2 c = 20 and a = 12
400 = b2 Simplify.
Example 1

15. 256 = b2 Subtract 144 from each side.
Perimeter and Area of a Parallelogram
256 = b2 Subtract 144 from each side.
16 = b Take the positive square root of each side.
The height is 16 in. UT is the base, which measures 32 in.
A = bh Area of parallelogram
= (32)(16) or 512 in2 b = 32 and h = 16
Answer: The perimeter is 104 in. and the area is 512 in2.
Example 1

16. A. Find the perimeter and area of
A. 88 m; 255 m2
B. 88 m; 405 m2
C. 88 m; 459 m2
D. 96 m; 459 m2
Example 1

17. Area of a Parallelogram
Find the area of
Step 1 Use a 45°-45°-90° triangle to find the height h of the parallelogram.
Example 2

18. Substitute 9 for the measure of the hypotenuse.
Area of a Parallelogram
Recall that if the measure of the leg opposite the 45° angle is h, then the measure of the hypotenuse is
Substitute 9 for the measure of the hypotenuse.
Divide each side by .
Example 2

19. A = bh Area of a parallelogram.
Step 2 Find the area.
A = bh Area of a parallelogram.
Multiply.
Answer: 76.4 square units
Example 2

20. Find the area of A. 156 cm2 B. 135.76 cm2 C. 192 cm2 D. 271.53 cm2
Example 2

21. Concept 3

22. Concept 4

23. Perimeter and Area of a Triangle
SANDBOX You need to buy enough boards to make the frame of the triangular sandbox shown and enough sand to fill it. If one board is 3 feet long and one bag of sand fills 9 square feet of the sandbox, how many boards and bags do you need to buy?
Example 3

24. Step 1 Find the perimeter of the sandbox.
Perimeter and Area of a Triangle
Step 1 Find the perimeter of the sandbox.
Perimeter = or 35.5 ft
Step 2 Find the area of the sandbox.
Area of a triangle
b = 12 and h = 7.1
Example 3

25. Perimeter and Area of a Triangle
Step 3 Use unit analysis to determine how many of each item are needed.
Boards
boards
Bags of Sand
Example 3

26. Round the number of boards up so there is enough wood.
Perimeter and Area of a Triangle
Round the number of boards up so there is enough wood.
Answer You will need 12 boards and 5 bags of sand.
Example 3

27. A. 12 boards and 14 bags of mulch B. 11 boards and 13 bags of mulch
PLAYGROUND You need to buy enough boards to make the frame of the triangular playground shown here and enough mulch to fill it. If one board is 4 feet long and one bag of mulch covers 7 square feet, how many boards and bags do you need to buy?
A. 12 boards and 14 bags of mulch
B. 11 boards and 13 bags of mulch
C. 12 boards and 13 bags of mulch
D. 11 boards and 14 bags of mulch
Example 3

28. Step 1 Find the perimeter of ∆ABC.
Perimeter and Area on the Coordinate Plane
Find the perimeter and area of △ABC with vertices A(4, –2), B(12, 6), and C(–4, 6).
Step 1 Find the perimeter of ∆ABC.
Use the distance formula to find the length of each side.
Example 4

29. Perimeter and Area on the Coordinate Plane
Example 4

30. Step 2 Find the area of ∆ABC.
Perimeter and Area on the Coordinate Plane
The perimeter of
△ABC is
or about 38.6 units.
Step 2 Find the area of ∆ABC.
Using
as the base, the height is the
perpendicular distance from A to
From the graph the height is 8 units.
Example 4

31. Substitute and simplify.
Perimeter and Area on the Coordinate Plane
Area of a triangle.
Substitute and simplify.
The area of ∆ABC is 64 square units.
Answer: or about 38.6 units; 64 units2
Example 4