11 -1 Area of Parallelograms and Triangles You

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.

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.

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

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. h b

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

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

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

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. Perimeter = RS + ST + UT + RU Area = 32 + 20 + 32 + 20 = 104 in. 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 202 = 122 + b 2 c = 20 and a = 12 400 = 144 + b 2 Simplify.

256 = b 2 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 = (32)(16) or 512 in 2 Area of parallelogram b = 32 and h = 16 Answer: The perimeter is 104 in. and the area is 512 in 2.

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

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

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 1 Find the perimeter of the sandbox. Perimeter = 16 + 12 + 7. 5 or 35. 5 ft Step 2 Find the area of the sandbox. Area of a triangle b = 12 and h = 9

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

Find the area of the figure. 7 4 49 24. 6 12. 3 7 35. 26 4. 3 8. 2

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

Area Formulas n Rectangle A = lw n Square A = s 2 n Triangle A = ½bh n Parallelogram A = bh

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