1. Areas of Parallelograms and Triangles
LESSON 11–1
Areas of Parallelograms and Triangles

2. Five-Minute Check (over Chapter 10) TEKS Then/Now New Vocabulary
Postulate 11.1: Area Addition Postulate
Key Concept: Area of a Parallelogram
Example 1: Perimeter and Area of a Parallelogram
Example 2: Area of a Parallelogram
Postulate 11.2: Area Congruence Postulate
Key Concept: Area of a Triangle
Example 3: Real-World Example: Perimeter and Area of a Triangle
Example 4: Use Area to Find Missing Measures
Lesson Menu

3. Mathematical Processes G.1(B), G.1(E)
Targeted TEKS
G.10(B) Determine and describe how changes in the linear dimensions of a shape affect its perimeter, area, surface area, or volume, including proportional and non-proportional
dimensional change.
Mathematical Processes
G.1(B), G.1(E)
TEKS

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

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

6. Concept 2

7. 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

8. 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

9. 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

10. 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

11. 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

12. 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 .
≈ 6.36 Simplify.
Example 2

13. A = bh Area of a parallelogram ≈ (12)(6.36) b = 12 and h = 6.36
Step 2 Find the area.
A = bh Area of a parallelogram
≈ (12)(6.36) b = 12 and h = 6.36
≈ 76.3 Multiply.
Answer: 76.3 square units
Example 2

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

15. Concept 4

16. 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

17. 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 = 9
Example 3

18. 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

19. 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 6 bags of sand.
Example 3

20. 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

21. Areas of Parallelograms and Triangles
LESSON 11–1
Areas of Parallelograms and Triangles