Notes Name Unit 5 Area of Rectangles and Irregular Figures Find the area of a rectangle that is 8 inches long and 3 inches wide. A. Use Counting Draw the rectangle on graph paper. Let each square represent 1 square inch. Count the squares inside the rectangle. There are 24 squares, so the area is 24 sq in. B. Use a Formula Use the formula for area. To find area, multiply length times width. A=ℓ×w A=8×3 A = 24 ℓ = length, w = width ℓ = 8, w = 3 The area of the rectangle is 24 sq in. A path around a garden measures 8 ft by 7 ft. The garden measures 4 ft by 3 ft. What is the area of the path? A. Use Counting Draw the figure on graph paper. Let each square represent 1 square foot. Count the squares in the path only. There are 44 squares, so the area is 44 sq ft. B. Use a Formula Find the area of the path and the garden together. Then subtract the area of the garden. Path: Display: A=ℓ×w A=ℓ×w A=8×7 A=4×3 A = 56 sq ft A = 12 sq ft 56 − 12 = 44, so the area is 44 sq ft. Find the area of each figure. 1. 2. 4. Suppose a rectangular path around a rectangular garden measures 4 meters by 7 meters. The garden measures 3 meters by 6 meters. What is the area of the path? 3. Name Area of Parallelograms and Triangles Find the area of this parallelogram. Find the area of this triangle. Use the formula A = bh. Use the formula A = A=8×6 A= A = 48 sq in. The area of the parallelogram is 48 sq in. 1 2 1 2 bh. × 10 × 8 A=5×8 A = 40 cm2 The area of the triangle is 40 cm2. Find the area of each parallelogram or triangle. 1. 2. 3. Triangle: b = 6 ft, h = 9 ft 4. Parallelogram: b = 18 m, h = 13 m 5. Triangle: b = 20 in., h = 9 in. 6. Writing to Explain Tony says he does not have enough information to find the area of this parallelogram. Is he correct? Explain. Massachusetts Comprehensive Assessment System Grade 6 Mathematics Reference Sheet CONVERSIONS 1 cup ! 8 fluid ounces 1 pint ! 2 cups 1 quart ! 2 pints 1 gallon ! 4 quarts 1 gallon ! 3.785 liters 1 liter ! 0.264 gallon 1 inch ! 2.54 centimeters 1 meter ! 39.37 inches 1 mile ! 5280 feet 1 mile ! 1760 yards 1 mile ! 1.609 kilometers 1 kilometer ! 0.62 mile 1 pound ! 16 ounces 1 pound ! 0.454 kilogram 1 kilogram ! 2.2 pounds 1 ton ! 2000 pounds 1 liter ! 1000 cubic centimeters AREA (A) FORMULAS VOLUME (V) FORMULAS square . . . . . . . . . . . A ! s 2 right rectangular prism . . . . . V ! lwh (l ! length; w ! width; h ! height) rectangle . . . . . . . . . A ! bh OR A ! lw parallelogram . . . . . A ! bh triangle . . . . . . . . . . A ! 1 bh 2 (b ! length of base; h ! height) circle. . . . . . . . . . . . A ! πr2 (r ! radius) CIRCLE FORMULAS area . . . . . . . . . . . . . A ! πr2 circumference. . . . . C ! 2πr OR C ! πd (d ! diameter) OR V ! Bh (B ! area of base; h ! height)
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