1. 11-1 Area of Parallelograms and Triangles You found areas of rectangles and squares. Find perimeters and areas of parallelograms. Find perimeters and areas of triangles.

2. Definitions A quadrilateral is a polygon with four sides. A parallelogram is a quadrilateral with two pairs of parallel sides. A rectangle is a quadrilateral with four right angles. A square is a quadrilateral with four right angles and four congruent sides.

3. What is the formula for the area of a rectangle? A = l × w l w

4. In the Area… Use the paper parallelogram, and label a base and height as shown. By cutting and rearranging pieces, use the area formula for a rectangle to help find the area formula for a parallelogram in terms of the length of the base and the height. b h

5. The area of a rectangle is the product of its length (l) and width (w). The area of a rectangle is the product of its length (l) and width (w). A = lw A = lw l w

6. The are of a square is the square of its side length (s). The are of a square is the square of its side length (s). A = s 2 A = s 2 s

7. p. 779 The area of a parallelogram is the product of its base length (b) and height (h). The area of a parallelogram is the product of its base length (b) and height (h). A = bh h b p. 779

8. Find the perimeter and area of PerimeterSince opposite sides of a parallelogram are congruent, RS UT and RU ST. So UT = 32 in. and ST = 20 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. c 2 = a 2 + b 2 Pythagorean Theorem 20 2 = 12 2 + b 2 c = 20 and a = 12 400= 144 + b 2 Simplify. Perimeter= RS + ST + UT + RU = 32 + 20 + 32 + 20= 104 in.

9. 256= b 2 Subtract 144 from eachside. 16= bTake the positive square root of each side. A= bhArea of parallelogram = (32)(16) or 512 in 2 b = 32 and h = 16 The height is 16 in. UT is the base, which measures 32 in. Answer: The perimeter is 104 in. and the area is 512 in 2.

10. A.88 m; 255 m 2 B.88 m; 405 m 2 C.88 m; 459 m 2 D.96 m; 459 m 2 A. Find the perimeter and area of

11. p. 781 The area of a triangle is half the product of its base length (b) and corresponding height (h). The area of a triangle is half the product of its base length (b) and corresponding height (h). A = ½bh A = ½bh b h

12. 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? Step 1Find the perimeter of the sandbox. Perimeter = 16 + 12 + 7.5 or 35.5 ft Step 2Find the area of the sandbox. Area of a triangle b = 12 and h = 9

13. Step 3Use unit analysis to determine how many of each item are needed. Boards Bags of Sand boards Answer: You will need 12 boards and 6 bags of sand. Round the number of boards up so there is enough wood.

14. Find the area of the figure. 7 7 49 8.2 4.3 35.26 12.3 4 24.6

15. What is a… quadrilateral? quadrilateral? A quadrilateral is a polygon with four sides. parallelogram? parallelogram? A parallelogram is a quadrilateral with two pairs of parallel sides. rectangle? rectangle? A rectangle is a quadrilateral with four right angles. square? square? A square is a quadrilateral with four right angles and four congruent sides.

16. Area Formulas RectangleA = lw Square A = s 2 TriangleA = ½bh ParallelogramA = bh

17. 11-1 Assignment Page 10-15 No formulas with numbers, no credit for the problem.