238 SQUARE MEASURE Figure A Figure B Figures A and B are' squares. How many sides has a square? Measure the sides of each figure. How many sides of Figure A are of the same length? Of Figure B? How many angles (corners) has the square? How many angles appear to be the same size? Fold a piece of paper to fit one of these angles. Can you make it fit the other angles? Can you tell what is meant by "square corners"? Describe a square in your own words. Cut from paper a one-inch square and a two-inch square. If the two-inch square were cut into two rectangles one inch wide, how long would each rectangle be? How many one-inch squares would be equal to one of these rectangles? Cut one of the rectangles to make two equal squares. Draw a four-inch square and show how many one-inch squares it contains. Compare the size of the four-inch square with that of the two-inch square. NOTE TO TEACHER: Square measure is often introduced into the fourth-grade to meet the needs of pupils grouped according to intelligence ratings. This topic may be omitted if the teacher desires. SQUARE MEASURE 239 Figure A Figure B Figure C Figure A is a one-inch square. Figure B is a rectangle one inch by two inches. Are the angles (corners) of the square and of the rectangles alike? Find objects in the schoolroom that have angles like those of the figures above. How many sides has a square? How many equal sides has it? How many angles has it? How many sides has each rectangle? How many pairs of equal sides has each? How many equal angles has a rectangle? As shown by the figures above, how many inch squares can you cut from the small rectangle? How many from the large rectangle? Figure A is one square inch. How many square inches in Figure B? How many square inches in Figure C? 240 AREAS OF RECTANGLES When we find how many times a unit of measure such as a square inch, a square foot, or a square yard is contained in a rectangle, we find the area. Figure A Figure B Figure C Figure A above is both a square and a rectangle. It is 1 unit long and 1 unit wide. Its area is 1 square unit. Figure B is a rectangle 4 units long and 1 unit wide. Its area is 4 square units. (4X1 sq. unit = 4 sq. units.) Figure C is a rectangle 4 units long and 2 units wide. What is its area in square units? (4X2 sq. units=?) Draw a rectangle that is 5 units long and 3 units wide. What is its area in square units? (5X3 sq. units = ?) How can you find the area of any rectangle if you know how many units long and how many units wide it is? The area of a rectangle is equal to the length multiplied by the width. Find the number of square units in the area of each rectangle mentioned below. Draw each rectangle. 1. A rectangle 2 units wide and 3 units long. 2. A rectangle 2 units wide and 5 units long. 3. A rectangle 3 units wide and 6 units long. 4. A rectangle 5 units wide and 6 units long. 5. A rectangle 7 units wide and 9 units long. 6. A rectangle 6 units wide and 8 units long. 7. A rectangle 4 units wide and 11 units long. SQUARE MEASURE 241 When you find the area of a surface you use square measure or surface measure. Areas of small surfaces such as walls, floors, and the tops of tables may be stated in square inches, square feet, or square yards. Figure A represents a square foot divided into square inches. How many square inches are in 1 row? How many rows are there? If there are 12 one-inch squares in 1 row, and there are 12 rows, how many one-inch squares are in the square foot? Explain Figure B. 144 square inches (sq. in.) = 1 square foot (sq. ft.) 2. How many square inches in 4 square feet? 3. How many square feet in 11 square yards? 4. Change 9 square yards to square feet. 1. A board is 2 feet wide and 16 feet long. How many square feet are in the board? 2. A room is 12 feet wide and 15 feet long. What is the area of the floor in square feet? In square yards? 3. What will it cost to floor the room mentioned in Problem 2 at 12¢ a square foot? 4. A walk is 8 feet wide and 24 feet long. How many square feet does it contain? 5. A house that has 220 square yards of surface was painted for $275.00. How much did each square yard of painting cost? 6. A garden is 16 yards wide and 30 yards long. How many square feet does it contain? 7. A tennis court is 36 feet wide and 78 feet long. How many square feet does it contain? 8. A lawn is 32 feet wide and 40 feet long. How many square feet are in the lawn? 9. A schoolroom is 24 feet wide and 32 feet long. How many square feet of floor space will there be for each child if the room contains 48 children? 10. At 30ć a square foot, what will be the cost of a pane of glass 24 inches wide and 30 inches long? 11. A kitchen 12 feet wide and 15 feet long was covered with linoleum at $1.55 a square yard. What was the cost of the linoleum? 12. A double garage floor 16 feet wide and 20 feet long is made of concrete. It cost 28¢ a square foot. What was the total cost of the floor? 13. A lawn 36 feet wide and 40 feet long was leveled and seeded at a cost of 60¢ a square yard. What was the total cost of the work? |