28. [Area / Volume] cm 2. in = =
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1 8. [ / Volume] Skill 8. Calculating the area of polygons by counting squares and triangles on a square grid (). Count the number of fully shaded squares on the grid. If necessary add on the number of half shaded squares (or triangles). Look for short cuts in your counting. Hint: To calculate the area of a rectangular shape it is possible to count the number of squares in a row and then multiply by the number of squares in a column. Q. Find the area of the rectangle. A. 6 There are 6 squares in a row cm and squares in a column. cm continues on page 66 MMBlue MMGreen cm a) Find the area of the triangle. b) Find the area of the rectangle. cm cm cm cm c) Find the area of the rectangle. d) Find the area of the rectangle. cm 0.5 in. cm in. page 65 Math s Mate Blue/Green Skill Builder 8
2 Skill 8. Calculating the area of polygons by counting squares and triangles on a square grid (). e) Find the area of the rectangle. f) Find the area of the polygon. continued from page 65 MMBlue MMGreen in. cm cm in. g) Find the area of the trapezoid. h) Find the area of the triangle. cm 0.5 in. cm in. i) Find the area of the parallelogram. j) Find the area of the trapezoid. cm cm cm cm page 66 Math s Mate Blue/Green Skill Builder 8
3 Skill 8. Comparing the area of polygons on a square grid (). Break the shape up into rectangles and triangles if necessary. Calculate the area of any rectangle by: Counting the squares OR Multiplying the number of squares in a row by the number of squares in a column. Calculate the area of any triangle by halving the area of the rectangle that would enclose it. Compare your results. Q. Do the rectangle and the triangle have the same area? A. A B No A 6 sq. units continues on page 68 MMBlue MMGreen A enclosing rectangle 3 B sq. units 3 B a) Do these rectangles have the same area? b) Do these rectangles have the same area? 4 A B A B yes 5 A... B... c) Do these polygons have the same area? d) Do these triangles have the same area? A... B... A... B... page 67 Math s Mate Blue/Green Skill Builder 8
4 Skill 8. Comparing the area of polygons on a square grid (). continued from page 67 MMBlue MMGreen e) Do these triangles have the same area? f) Do these triangles have the same area? A... B... A... B... g) Do these triangles have the same area? h) Do these triangles have the same area? i) Do these polygons have the same area? j) Do these polygons have the same area? k) Do the square and the parallelogram have the same area?... l) Do the parallelogram and the kite have the same area? page 68 Math s Mate Blue/Green Skill Builder 8
5 Skill 8.3 Estimating the area of irregular shapes on a square grid. MMBlue MMGreen Break the shape up into workable parts (rectangles/triangles/curved shapes). Calculate the area of any rectangle by: Counting the squares OR Multiplying the number of squares in a row by the number of squares in a column. Calculate the area of any triangle by halving the area of the rectangle that would enclose it. Estimate the area of any partly curved shape by making up whole squares from the shaded region. Add the results. Q. Find the area of the shaded shape. [Round to the nearest whole number.] A. A + B sq. units A 4 whole units A B 9 units (made up from part units) B a) Find the area of the shaded shape. [Round to the nearest whole number.] b) Find the area of the shaded shape. [Round to the nearest whole number.] A B A 7 and B... A + B sq. units A and B... A + B... sq. units c) Find the area of the shaded shape. [Round to the nearest whole number.] d) Find the area of the shaded shape. [Round to the nearest whole number.] sq. units sq. units page 69 Math s Mate Blue/Green Skill Builder 8
6 Skill 8.4 Calculating the area of squares, rectangles and parallelograms (). Use the appropriate formula. square A l l l Q. Using A lw find the area of the rectangle. 6 cm l length rectangle A l w lw. l length w width parallelogram A b h bh A. A lw where l 6 and w cm b base continues on page 7 MMBlue MMGreen h height a) Using length width find the area of this rectangle. b) Using length width find the area of this rectangle. cm cm 6 cm 7 cm A 7 cm A cm c) Using base height find the area of this parallelogram. d) Using base height find the area of this parallelogram. cm A cm A cm e) Using length width find the area of this rectangle. 0.5 in. f) Using A lw find the area of the rectangle. mm in. 50 mm A in. A mm page 70 Math s Mate Blue/Green Skill Builder 8
7 Skill 8.4 Calculating the area of squares, rectangles and parallelograms (). g) Using length length find the area of the square. continued from page 70 MMBlue MMGreen h) Using l find the area of this square..5 in. cm A A in. i) Find the area of the square. j) Using base height find the area of the parallelogram. 0 mm 3.. mm A A cm k) Using base height find the area of the parallelogram. l) Using A lw find the area of the rectangle. 0 mm 6 mm 40 mm b 60 mm mm A A mm m) Using A bh find the area of the parallelogram. 55 mm 0 mm n) Find the area of this parallelogram. 0 mm 36 mm mm A A mm page 7 Math s Mate Blue/Green Skill Builder 8
8 Skill 8.5 Calculating the area of triangles (). Use the formula. Q. Using base height find the area of the triangle. cm triangle b base h height A b h bh A. A bh where b 6 and h 6 6 cm continues on page 73 MMBlue MMGreen cm a) Using base height find the area of the triangle. in. b) Using base height find the area of the triangle. in. 7 cm A... 4 in. c) Using base height find the area of the triangle. A... cm d) Using A bh find the area of the right triangle. 50 mm 5 mm A... A... cm mm page 7 Math s Mate Blue/Green Skill Builder 8
9 Skill 8.5 Calculating the area of triangles (). e) Using base height find the area of the triangle. continued from page 7 MMBlue MMGreen f) Using bh find the area of the triangle.. 5 mm 0 mm A... A... cm mm g) Using base height find the area of the triangle. h) Using bh find the area of the triangle. cm 7. A... 0 mm 40 mm A... cm mm i) Using bh find the area of the triangle. 0 mm j) Using bh find the area of the triangle. 55 mm 7 mm 30 mm A... A... mm mm page 73 Math s Mate Blue/Green Skill Builder 8
10 Skill 8.6 Calculating the volume of rectangular prisms by counting cubes (). Count the cubes. Hint: Count the cubes in one layer and then multiply the result by the total number of layers. continues on page 75 MMBlue MMGreen Q. Find the volume of the rectangular prism. A. V cubes in top layer 5 layers all together Vol 8 cm cm a) Find the volume of the rectangular prism. b) If 4 boxes can fit inside these shelves, find the total volume of the boxes. Vol box Vol 50 in. 3 6 cm V 4 3 V in. 3 c) Find the volume of the rectangular prism. d) Find the volume of the rectangular prism. Vol cm 0 cm Vol V V e) Find the volume of the rectangular prism. f) Find the volume of the rectangular prism. Vol cm Vol 9 cm V V page 74 Math s Mate Blue/Green Skill Builder 8
11 Skill 8.6 Calculating the volume of rectangular prisms by counting cubes (). continued from page 74 MMBlue MMGreen g) Find the volume of the rectangular prism. h) Find the volume of the rectangular prism. Vol 8 cm Vol 6 cm V V i) Find the volume of the rectangular prism. j) Find the volume of the rectangular prism. Vol 9 cm Vol 0 cm V V k) Find the volume of the rectangular prism. l) Find the volume of the rectangular prism. Vol 9 cm Vol 7 cm V V page 75 Math s Mate Blue/Green Skill Builder 8
12 Skill 8.7 Calculating the volume of square and rectangular prisms (). Use the appropriate formula. cube V l l l l 3 square prism V l l h l h l length h height l length rectangular prism V l w h lwh continues on page 77 MMBlue MMGreen h height w width l length Q. Using V l h find the volume of the square prism.. A. V a) Using V lwh find the volume of the rectangular prism. b) Using V l h find the volume of the square prism. 0 mm 70 mm mm l cm h V ,800 mm 3 V... c) Using V l h find the volume of the square prism. d) Using V l 3 find the volume of the cube. l 0 mm in. V in. V... in. 3 mm 3 page 76 Math s Mate Blue/Green Skill Builder 8
13 Skill 8.7 Calculating the volume of square and rectangular prisms (). e) Using V lwh find the volume of the bank of lockers that is a rectangular prism. 6 ft 0 ft ft V... ft 3 f) Using V lwh find the volume of the rectangular prism. 60 mm V... continued from page 76 MMBlue MMGreen mm 5 mm mm 3 g) Using V l 3 find the volume of the cube. h) Using V lwh find the volume of the rectangular prism. 5 mm V... i) Using V l h find the volume of the square prism. mm 3. V... j) Using V l h find the volume of the square prism. l. h cm l 30 mm V... h 0 mm V... mm 3 page 77 Math s Mate Blue/Green Skill Builder 8
14 Skill 8.8 Calculating the area of composite shapes (). Break the shape up into workable parts (rectangles/triangles). Calculate the area of each part. (see skill 8.4, page 70 and skill 8.6, page 74) Add the results. continues on page 79 MMBlue MMGreen Q. Find the area of the shaded polygon. A. A lw where l 4 and w A bh where b 5 and h A 3 bh where b 3 and h A A + A + A sq. units A A A 3 a) Find the area of the shaded polygon. b) Find the area of the shaded polygon. 3. cm cm 3. cm cm cm A A A A... A cm A A... A sq. units c) Find the area of the shaded polygon. d) Find the area of the shaded polygon. A A... A sq. units A A... A sq. units page 78 Math s Mate Blue/Green Skill Builder 8
15 Skill 8.8 Calculating the area of composite shapes (). continued from page 78 MMBlue MMGreen e) Find the area of the shaded polygon. f) Find the area of the shaded polygon. A A... A A A sq. units... A sq. units g) Find the area of the bowtie. h) Find the area of the polygon. 8 cm 0 cm A A... A... cm cm A A... A... cm i) Find the area of the shaded polygon. j) Find the area of the polygon. 0 mm in. mm 7 mm mm.5 in. in. A A A A A... mm A in.... page 79 Math s Mate Blue/Green Skill Builder 8
16 Skill 8.9 Calculating the area of trapezoids and rhombii. Use the appropriate formula. trapezoid b h a A (base a + base b) height h (a + b)h Q. Using A (a + b)h find the area of the trapezoid. cm 6 cm rhombus A diagonal a diagonal b ab continues on page 8 A. A (a + b)h where a 3, b 6 and h (6 + 3) 9 9 cm a b l MMBlue MMGreen a) Using A ab find the area of the rhombus. A mm c) Using A (a + b)h find the area of the trapezoid. b 6 cm cm 4 mm a 56 mm A... cm b) Using (base a + base b) height find the area of the trapezoid. a 30 mm 0 mm b 45 mm A... mm d) Using diagonal a diagonal b find the area of the rhombus. a 50 mm b 5 mm A... mm page 80 Math s Mate Blue/Green Skill Builder 8
17 Skill 8.0 Calculating the area of circles and composite circular shapes. Use the formula. Hint: If you are given the diameter then halve to find the radius: Q. Using A πr and π 3.4, find the area of the semi-circle. 0 mm circle a) Using A πr and π 3.4, find the area of the shaded shape. 6 cm cm radius A π radius radius where π πr or 7 d r MMBlue MMGreen A. of circle πr where d 0 and r of semi-circle mm d r b) Using A πr and π, find the area of the circle. 7 6 cm A cm mm A If d 6 then r 3 A A 6 6 and using A A + A... A for the semi-circle cm A mm d) Using A πr and π 3.4, find the area of the shaded shape. c) Using A πr and π 3.4, find the area of the semi-circle. cm A... cm A... A... A cm page 8 Math s Mate Blue/Green Skill Builder 8
18 Skill 8. Calculating the volume of any prism. Use the general formula. prism h MMBlue MMGreen V of base height of prism Bh B Q. Using V Bh find the volume of the prism. A. A Bh where B 50 and h mm 3 B 50 mm 0 mm a) Using V Bh find the volume of the triangular prism. b) Using Volume area of the base height of the prism, find the volume of the pentagonal prism. h 0 mm 5 mm 0 mm h cm B B 8. V 50 0 c) Using V Bh find the volume of the hexagonal prism. mm 3 V d) Using V Bh find the volume of the prism. B 7 ft h 8 ft B 660 mm 5 mm V e) Using V Bh find the volume of the triangular prism.. B... V h ft 3 mm 3 V f) Using V Bh find the volume of the triangular prism. 30 mm 60 mm 0 mm B... mm 3 V page 8 Math s Mate Blue/Green Skill Builder 8
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