MEA 501 LESSON _NOTES Period. CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must MEA 301 Compute the perimeter of polygons when all

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1 MEA 501 LESSON _NOTES Period Name CRS SKILL LEVEL DESCRIPTION Level 1 ALL students must MEA 301 Compute the perimeter of polygons when all attain mastery at this level side lengths are given MEA 302 Compute the area of rectangles when whole number dimensions are given MEA 401 Compute the area and perimeter of triangles and rectangles in simple problems MEA 501 Level 1 Level 2 MOST students will attain mastery of the focus skill in isolation. Level 3 SOME students will attain mastery of focus skill with other skills Level 4 SOME students will attain mastery of focus topics covered in a more abstract way Level 5 FEW students will attain mastery of the extension skill. 1. Find the area and perimeter of the figure below. MEA 501 Compute the area of triangles and rectangles when one or more additional simple steps are required MEA 601 Use relationships involving area, perimeter, and volume or geometric figures to compute another measure VOCABULARY Parallelogram, Trapezoid, Rhombi, Kite, Prism, Cone, Pyramid, Surface Area, Volume, Slant Height REQUIRED SKILL TO MASTER Area of triangles; Area of triangles 2; Area of parallelograms, Additional Practice on KHAN Area of trapezoids, rhombi, kites; Area of quadrilaterals and polygons; Nets of 3D figures; Surface area using nets; Surface area; Area, volume, and surface area;2d geometric models; Perimeter= Area= 1

2 Parallelogram Cut out a parallelogram and trace it below. Measure and label the sides to the nearest tenth of a centimeter. Then find the perimeter. Then cut off the left side as indicated in the diagram and tape the rearranged parallelogram below. Measure the height of the parallelogram. Then find the area of the parallelogram. 2. For each parallelogram below find the perimeter and area. In each drawing the vertical dashed line is perpendicular to the base. a) A B T R D C TR = 3.1 cm AB = 4.3 cm AD = 15.3 cm b) W J K JY = 2.2 cm XW = 2.5 cm XM = 7.0 cm c) Z P U UQ = 6.7 cm LZ = 8.1 cm LS = 2.9 cm X Y M L Q S 2

3 Triangle Cut out a triangle and trace it below. Measure and label the sides to the nearest tenth of a centimeter. Then find the perimeter. Then cut out a second triangle the same size and tape the two triangles below so they form a parallelogram. Measure the height of the parallelogram. Then find the area of the parallelogram. Finally find the area of the triangle. 3. For each triangle below find the perimeter and area. a) v = 32 cm d = 6 cm z = 27 cm m = 39 cm b) e=46cm v = 40 cm f =23 cm d = 19 cm 4. A farmer builds 3 rectangular pens for hogs. Each pen measure 30 ft by 12 ft. Find the total area available for the hogs. 3

4 5. The Yield sign has 48- inch edges and a height of 42 inches. Each side is treated with spray sealant to make it last longer. How much area will the sealant need to cover if both sides of the sign need to be sealed? Trapezoid Cut out a trapezoid and trace it below. Measure and label the sides to the nearest tenth of a centimeter. Then find the perimeter. Then cut out a second trapezoid the same size and tape the two trapezoids below so they form a parallelogram. Measure the height of the parallelogram. Then find the area of the parallelogram. Finally find the area of the trapezoid. 6. What is the area in square feet, of a trapezoid with a height of 4 feet and parallel basses of 7 feet and 5 feet? 4

5 7. For each trapezoid below find the perimeter and area. B C EB = 6.05 cm AD = 3.31 cm BA = 6.17 cm BC = 7.54 cm CD = 8.16 cm G H K I J GH = 5.99 cm HI = 2.30 cm IJ = 3.80 cm JG = 9.67 cm KH = 3.08 cm A E D 8. The shape of the state of Arkansas resembles a trapezoid. Find the approximate area of Arkansas. Kite Cut out a kite and trace it below. Measure and label the sides to the nearest tenth of a centimeter. Then find the perimeter. Then cut the kite as indicated in the diagram and tape the kite pieces below to create a rectangle. Measure the length and width of the rectangle. Note one side will be a diagonal and the other side will be equal to ½ the length of the other diagonal. Then find the area of the parallelogram. 5

6 9. Find the area and perimeter of each kite below. a) b) g = 30 cm 32.7 cm g = 29 cm 34.1 cm t 1 = 13 cm 13 cm t 1 = 18 cm 18 cm f = 2 cm 13.2 cm f = 2 cm 18.1 cm Regular Polygon Cut out a polygon and trace it below. Measure and label the sides to the nearest tenth of a centimeter. Then find the perimeter. Trace lines on the regular polygon to show the congruent isosceles triangles. Measure the height, and base of any one of the triangles. Then find the area of the regular polygon. 6

7 10. Find the area and perimeter of each regular polygon below. a) b) r = 8 cm e = 7 cm e = 6 cm r = 7 cm 11. The formula of the volume of the brick is where l is the length, w is the width and h is the height of the brick. A construction worker purchased bricks that have a volume of 36 cubic centimeters. She is trying to determine how many bricks to lie on a patio. She knows that the height of a brick is 3 centimeters and the width is 2 centimeters. What is the length? 7

8 12. The surface area of a rectangular prism is given use the formula SA = 2lw + 2lh + 2wh where l is the length, w is the width, and h is the height of the prism. Find the surface area of a prism with a length of 3 m, a width of 2 m, and a height of 6 m. Level The page of a book measures 8 inches by 6 inches. There is one inch of white space around the text in every direction. How many square inches of text are on each page? 14. A swimming pool that is 25 ft. long and 15 ft. wide is having trim installed around the outer edge of the pool. How many feet long will this trim be? 8

9 15. The same swimming pool that is 25 ft. long and 15 ft. wide is having a cover made that is one foot longer and one foot wider than the pool. How many square feet is this pool cover? 16. Note: There is often more than one way to solve a complex area problem. Find the area of the figure to the right using at least two different methods. All units are in feet. 17. For each triangle below find the perimeter and area. (Hint: to find the perimeter of b you will need to do the Pythagorean theorem twice.) a) g = 43 cm f = 21 cm b) h = 12 cm j =14 cm g = 36 cm 18. Find the area and perimeter of each kite below. 9

10 19. Find the perimeter and area of this trapezoid. Level The company Digit Tech designs a new SmartPhone. The packaging includes an open box (no top) made out of cardboard. The dimensions of the box are 15 cm long, 10 cm wide, and 10 cm high. Digit Tech expects to sell 1000 phones and package each phone individually in a box. In square centimeters, what is the minimum amount of cardboard Digit Tech needs to package all 1000 new SmartPhones? (Assume there is no wasted cardboard.) 21. Cement sheeting is to be used to cover the external wall of this shed. The doorway is 900mm by 800 mm and the window is 1200 mm by 600 mm, and these are not to be covered. How many square meters of cement sheeting will be on the finished wall? Give your answer to the nearest tenth of a square meter. 10

11 22. Elizabeth purchased an irregular block of land on which to build a house. The price was $150,000. a. Calculate the area of land, to the nearest square meter. b. Real- estate values are often given as a dollar cost per square meter. What is this figure for Elizabeth s place? 23. A swimming pool is 8 m long, 6 m wide, and 1.5 m deep. The paint needed for the pool costs $6 per square meter. How much will it cost to paint the interior surfaces of the pool? 24. A local movie theater is trying to decide what size bag to use for the popcorn it sells. Which bag would hold the grater amount of popcorn? Bag A measures: " long, 7" high and " wide Bag B measures: 5" long, " high and " wide Level The width of a rectangle is twice the length. The perimeter is 104 feet. Find the dimensions. 26. If one side of a square is increased by 8 cm and an adjacent side decreased by 2 cm, a rectangle is formed whose perimeter is 40 cm. Find the length and width of the rectangle. 27. A pool has a perimeter of 176 ft. and a length that is three times the width. What is the area of the pool? 11

12 Level 5 (Please see math reference sheet for many formulas needed in this class.) 28. Find the surface area and volume of the prism. 29. Use the diagram at the right. a. What is the height of the solid? b. What is the area of the base? c. What is the perimeter of a base? d. What is the surface area of the solid? e. What is the volume of the solid? 2. If 1 cm 3 of iron has a mass of 7.52 g, what is the mass of an iron bar of rectangular cross section with the dimensions shown? 30. A library has an aquarium in the shape of a rectangular prism. The base is 6 ft by 2.5 ft. The height is 4 ft. How many square feet of glass was used to build the aquarium? 12

13 31. Find the surface area and volume of the pyramid. 32. Find the surface area and volume of the pyramid. 13

14 Shape Perimeter Area Rectangle l w Parallelogram Triangle e h d Trapezoid h b2 b b1 Kite d 2 d1 b a Regular Polygon a s 14