1. Entry Task Find the unknown side length in each right triangle with legs a and b and hypotenuse c. 1. a = 20, b = 21 2. b = 21, c = 35 c = 29 a = 28

2. Entry Task P. 611 #16, 17 #16 3/5 #16 5 bags

3. I can develop and apply the formulas for the areas of triangles and parallelograms. 10-1 Areas of Parallelograms and Triangles Learning Target

4. Dot paper Get a piece of dot paper Cut out a parallelogram that is at least 4 inches by 5 inches big

5. Remember that rectangles and squares are also parallelograms. The area of a square with side s is A = s 2, and the perimeter is P = 4s.

7. Recall that a rectangle with base b and height h has an area of A = bh. You can use the Area Addition Postulate to see that a parallelogram has the same area as a rectangle with the same base and height.

8. Find the area of the parallelogram. Example 1A: Finding Measurements of Parallelograms Step 1 Use the Pythagorean Theorem to find the height h. Step 2 Use h to find the area of the parallelogram. Simplify. Substitute 11 for b and 16 for h. Area of a parallelogram 30 2 + h 2 = 34 2 h = 16 A = bh A = 11(16) A = 176 mm 2

9. Check It Out! Example 1 A = bh Find the base of the parallelogram in which h = 56 yd and A = 28 yd 2. 28 = b(56) 56 b = 0.5 yd Area of a parallelogram Substitute. Simplify.

11. Check It Out! Example 2 Find the area of the triangle. Find b. A = 96 m 2 Substitute 16 for b and 12 for h. Area of a triangle Simplify.

12. Homework p. 619 8,11,14,15,17,18,21,22 Challenge - 44

15. Example 2B: Finding Measurements of Triangles and Trapezoids Find the base of the triangle, in which A = (15x 2 ) cm 2. Sym. Prop. of = Divide both sides by x. Substitute 15x 2 for A and 5x for h. Area of a triangle 6x = b b = 6x cm Multiply both sides by

18. Check It Out! Example 4 In the tangram, find the perimeter and area of the large green triangle. Each grid square has a side length of 1 cm. The area is A = 4cm 2. The perimeter is P = (4 + 4 ) cm.

19. Lesson Quiz: Part I Find each measurement. 1. the height of the parallelogram, in which A = 182 mm 2 h = 9.1 mm 2. the perimeter of a rectangle in which h = 8 in. and A = 28x in 2 P = (16 + 7x) in.

20. Lesson Quiz: Part II 3. the area of the trapezoid A = 16.8x ft 2 4. the base of a triangle in which h = 8 cm and A = (12x + 8) cm 2 b = (3x + 2) cm 5. the area of the rhombus A = 1080 m 2

21. Lesson Quiz: Part III 6. The wallpaper pattern shown is a rectangle with a base of 4 in. and a height of 3 in. Use the grid to find the area of the shaded kite. A = 3 in 2

22. Example 4: Games Application The tile design shown is a rectangle with a base of 4 in. and a height of 2 in. Use the grid to find the perimeter and area of the leftmost shaded parallelogram. in. Perimeter: Two sides of the parallelogram are vertical and the other two sides are diagonals of a square of the grid. Each grid square has a side length of 1 in., so the diagonal is The perimeter of the leftmost shaded parallelogram is P = 2(1)+2( ) = (2 + 2 ) in.

23. Example 4 Continued The tile design shown is a rectangle with a base of 4 in. and a height of 2 in. Use the grid to find the perimeter and area of the leftmost shaded parallelogram. in. Area: The base and height of the leftmost shaded parallelogram each measure 1 in., so the area is A = bh = (1)(1) = 1 in 2.