G6-9 Area of Composite Shapes 1. a) Calculate the area of each figure. b) Draw a line to show how Shape C can be divided into rectangles A and. i) ii) A C A C Area of A = Area of A = Area of = Area of = Area of C = Area of C = iii) A C iv) A C Area of A = Area of A = Area of = Area of = Area of C = Area of C = c) How can you get the area of C from the areas of A and? Write an equation. Area of C = 2. Draw a line to divide the figure into two rectangles. Use the areas of the rectangles to find the total area of the figure. a) 4 m b) 10 cm c) 2 in 3 m 4 cm 5 in 7 cm 7 m 4 m 6 cm 8 in 3 cm 4 m 7 in 4 cm 8 m 9 in Area of Rectangle 1 = Area of Rectangle 1 = Area of Rectangle 1 = Area of Rectangle 2 = Area of Rectangle 2 = Area of Rectangle 2 = Total area = Total area = Total area = 3 in 162 Geometry 6-9
3. a) A building is 8 stories high. The wing is b) The tower of a building is 10 m wide. The 5 stories high. How many stories high is base is 50 m wide. How wide is the wing? the tower? 10 m tower The tower is stories high. tower The wing is m wide. 6 8 stories wing 5 stories wing 50 m 4. Find the missing side lengths. Divide the figure into two rectangles and find their areas. Then find the total area of the figure. a) 2 m b) 3 ft 6 m 4 m 3 ft 6 ft 4 ft 6 m Area of Rectangle 1 = Area of Rectangle 1 = Area of Rectangle 2 = Area of Rectangle 2 = Total area = Total area = 5. The picture shows plans for two flowerbeds. Find the area and the perimeter of each flowerbed. Flowerbed A Flowerbed 3 ft A Area = Area = Perimeter = Perimeter = Which flowerbed has greater area? Which has greater perimeter? 6. The picture shows plans for two parks. Find the area and the perimeter of each park. Park A Park Area = Area = 0.5 km A Perimeter = Perimeter = Geometry 6-9 163
G6-10 Area of Parallelograms 1. Move the shaded triangle to make a rectangle with the same area as the parallelogram. Find the base and the height of the parallelogram and the width and the height of the rectangle. a) 5 b) ase = 4 Width = ase = Width = c) ase = Width = d) ase = Width = 2. a) Look at your answers in Question 1. Complete each sentence with the word base or height. The height of the rectangle is the same as the The width of the rectangle is the same as the b) Area of rectangle = width height. What is the formula for the area of a parallelogram? Area of parallelogram = of the parallelogram. of the parallelogram. 164 Geometry 6-10
Area of parallelogram = base height or A = b h 3. Find the area of the parallelogram given the base and height. a) ase = 5 cm b) ase = 4 cm c) ase = 8 cm d) ase = 3.7 cm 7 cm 3 cm 6 cm 6 cm Area = Area = Area = Area = Any side of a parallelogram can be used as a base. The height is always perpendicular to the base. ase Height Height ase Height ase 4. Find the area in two ways, by using different sides as base. Use a ruler. ase = ase = Area = Area = 5. Draw a perpendicular to the base of each parallelogram (thick line) using a protractor or a square corner. Measure the height and the base of the parallelogram. Find the area of the parallelogram. Area = Area = 6. A bus has ten windows that are parallelograms with height 1 m and base 1.3 m. Glass costs $23 for each 1 m 2. How much will it cost to replace the glass in all ten windows? Geometry 6-10 165
G6-11 Area of Triangles Two identical right triangles make a rectangle. Area of right triangle = Area of rectangle 2 = 2 1. Find the area of the triangle in square units. a) b) c) d) Area = Area = Area = Area = 2. Draw a line to divide the triangle into two right triangles. Find the areas of all the triangles in square units. a) b) c) d) Triangle 1 = 6 Triangle 1 = Triangle 1 = Triangle 1 = Triangle 2 = 2 Triangle 2 = Triangle 2 = Triangle 2 = Total area = 8 Total area = Total area = Total area = 3. Rectangle C is made of rectangles A and. Triangle C is made of triangles A and. a) Find the areas. A Area of Rectangle A = Area of Triangle A = Area of Rectangle = Area of Triangle = Area of Rectangle C = Area of Triangle C = b) What fraction of the area of Rectangle C is the area of Triangle C? 4. Juan says: The area of Triangle T is half of the area of the rectangle. Is he correct? Explain. T C 166 Geometry 6-11
Triangles have base and height. Height is measured along a perpendicular to the base. height base 5. a) Find the base and the height of each triangle. Then fill in the table. ase of triangle 5 Height of triangle 4 Width of rectangle 5 Height of rectangle 4 Area of rectangle 20 Area of triangle 10 b) Look at the table in part a). Complete each sentence with the word base or height. The height of the rectangle is the same as the The width of the rectangle is the same as the of the triangle. of the triangle. Area of triangle = base height 2 or A = b h 2 6. Find the area of the triangle given the base and height. Do not forget the units. a) ase = 5 cm b) ase = 4 cm c) ase = 8 cm d) ase = 3.7 cm 8 cm 3 cm 6 cm 6 cm Area = Area = Area = Area = 7. Find the area of the triangle. a) b) c) d) 3 ft 6 in 8 ft 5 m 4.5 in 12 in 7 m 6 in Area = Area = Area = Area = Geometry 6-11 167
G6-12 Area of Triangles and Parallelograms REMINDER Area of parallelogram = base height or A = b h 1. Hank joined two copies of Triangle A together to make Parallelogram. a) What should he do to find the area of Triangle A from the area of Parallelogram? A Area of = Area of A = Area of = b) Find the area of triangles C and D using Hank s method. C D Area of parallelogram = Area of parallelogram = Area of C = Area of D = c) Look at your answers in parts a) and b). Complete each sentence with the word base or height. The height of the triangle is the same as the of the parallelogram. The base of the triangle is the same as the of the parallelogram. d) Write the formula for the area of a triangle using the base and the height of the triangle. Area of triangle = 2. Measure the base and height of the triangle. Then find the area of the triangle. a) b) c) ase = ase = ase = Area = Area = Area = 168 Geometry 6-12
3. Find the area of the triangle with these dimensions. a) ase = 6 cm b) ase = 4 in c) ase = 6 ft d) ase = 3.2 cm 2 cm 6 in 3 ft 8 cm Area = Area = Area = Area = 4. In each triangle, the thick line is the base. Use a square corner or a protractor to draw the height. Then measure the bases and the heights and fill in the table. ase Height Area 5. a) A company s logo is a triangle with base 6 ft and height 4 ft. What is its area? b) A park is a right triangle with base 2 km and height 1.5 km. What is its area? c) A plot of land is a triangle with base 37 yd and height 40 yd. What is its area? 6. Plot the points on the grid, then find the area of the Triangle AC. a) A (1, 1), (5, 1), C (4, 5) b) A (1, 0), (5, 0), C (4, 2) y y 5 5 4 4 3 3 2 2 1 1 0 x 0 x 0 1 2 3 4 5 0 1 2 3 4 5 c) A (0, 4), (8, 0), C (8, 4) d) A (6, 2), (6, 5), C (2, 4) 7. a) Find the base, the height, and the area of each triangle. What do you notice? b) On grid paper, draw two different triangles with the same base and height. What do you know about their areas? Geometry 6-12 169
G6-13 Area of Trapezoids and Parallelograms A trapezoid is a quadrilateral with exactly one pair of parallel sides. These sides are both called bases. trapezoids not trapezoids height base base 1. Split the trapezoid into a triangle and a rectangle, then find the area of each shape in square units. a) b) c) d) Area of a) rectangle = 12 b) rectangle = c) rectangle = d) rectangle = triangle = 3 triangle = triangle = triangle = trapezoid = 15 trapezoid = trapezoid = trapezoid = 2. Split the trapezoid into two triangles and a rectangle, then find the area of each shape in square units. a) b) c) d) Area of a) rectangle = 6 b) rectangle = c) rectangle = d) rectangle = triangle 1 = 1.5 triangle 1 = triangle 1 = triangle 1 = triangle 2 = 3 triangle 2 = triangle 2 = triangle 2 = trapezoid = 10.5 trapezoid = trapezoid = trapezoid = 3. a) What is the base of the triangle? b) What is the area of the trapezoid? 4 cm 2 cm 5 cm 170 Geometry 6-13
4. Draw an upside down copy of each trapezoid, as shown in part a), to create a parallelogram. Then fill in the blanks for each parallelogram. A C a) length of base = 6 4 + 2 b) length of base = c) length of base = height = 3 height = height = 5. A trapezoid has the bases given. If you make a parallelogram as in Question 4, what will the base of the parallelogram be? a) bases of trapezoid = 2 cm and 3 cm base of parallelogram = cm b) bases of trapezoid = 5 m and 7 m base of parallelogram = c) bases of trapezoid = 4 in and 6 in base of parallelogram = REMINDER Area of parallelogram = base height or A = b h 6. Find the areas of the parallelograms in Question 4. a) Area of parallelogram = b) Area of parallelogram = c) Area of parallelogram = 7. a) How many trapezoids make up each parallelogram in Question 4? b) Area of trapezoid = area of parallelogram c) Write an equation for the area of each trapezoid in Question 4. sum of bases height A: (4 + 2) 3 2 : ( + ) 2 C: ( + ) 2 = 6 3 2 = = 2 = = 2 = 8. Finish writing a formula for the area of a trapezoid: Area of trapezoid = (base 1 + base 2) 9. Find the area of the trapezoid. 1 a) 3 m b) 8 m c) 3 ft 2 3 m 2 m 5 m 4 ft 6 1 2 ft 7 m Geometry 6-13 171