# Areas of Polygons. Goal. At-Home Help. 1. A hockey team chose this logo for their uniforms.

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1 -NEM-WBAns-CH // : PM Page Areas of Polygons Estimate and measure the area of polygons.. A hockey team chose this logo for their uniforms. A grid is like an area ruler. Each full square on the grid has an area of square unit. Many shapes drawn on grids can be divided into squares and right-angled triangles. For example: a) Estimate the area in square units. Suggested answer: square units b) Measure the area in square units.. square units. For each polygon, estimate and then measure the area in square units. Estimated area In this shape, there are full squares (lightly shaded) and half squares (darkly shaded). So the total area is square units. Measured area a) Suggested answer: square units. square units b) Suggested answer: square units 9 square units c) Suggested answer: square units 9. square units Copyright by Thomson Nelson Answers Chapter : Area and Grids

2 -NEM-WBAns-CH // : PM Page Areas of Irregular -D Shapes Develop methods to measure the areas of irregular -D shapes. Find the area of this tulip shape to the nearest square unit using each of the methods below. A grid is useful when measuring the area of an irregular -D shape to the nearest square unit. On centimetre grid paper, each full square has an area of square centimetre. Part squares that cover less than half a square can be rounded down. Part squares that cover more than half a square can be counted as full square. Part squares can also be grouped to make up about full square. For example:. Count the full squares. For part squares, if less than half a square is covered, round down. If more than half a square is covered, round up. Full squares Part squares Total area square units. Count the full squares. For part squares, count how many squares you could make by putting together the part squares. Full squares Part squares Total area 9 square units. Count the full squares. For part squares, count only those that are half or more. This circle covers full or almost full squares (lightly shaded). There are remaining part squares (darkly shaded), which can be grouped to give about more full squares. So the total area of the circle is about square units. Full squares Part squares Total area square units Answers Chapter : Area and Grids Copyright by Thomson Nelson

3 -NEM-WBAns-CH // : PM Page Relating Perimeter and Area of Rectangles Explore relationships among side lengths, perimeter, and area of rectangles. Camille has cm of decorative tape to put around the perimeter of a bookmark.. Sketch all possible rectangles she can design with a perimeter of cm. Perimeter is the distance around a shape. Rectangles with the same area may have different perimeters. For example: Both rectangles have an area of cm, but the perimeter of both rectangles is not the same. The top rectangle has a perimeter of cm while the bottom rectangle has a perimeter of cm. Rectangles with the same perimeter may have different areas.. Calculate the area of each rectangle in Question. Record your answers in the table. Length of Length of side (cm) side (cm) Area (cm ) cm 9 cm 9 cm cm cm cm cm cm cm cm cm cm cm cm cm Both rectangles have a perimeter of cm, but the area of both rectangles is not the same. The top rectangle has an area of cm while the bottom rectangle has an area of cm. Perimeter is an outside measurement while area is an inside measurement.. How are the areas and the shapes of the rectangles related? The areas of the rectangles increase as side length gets close to side length. This means that the areas increase as the rectangles get close to becoming a square. Copyright by Thomson Nelson Answers Chapter : Area and Grids

4 -NEM-WBAns-CH // : PM Page Area Rule for Rectangles Develop and explain a rule for calculating the area of a rectangle.. Jasmine is choosing address labels. Calculate each area. Use the rule for area of a rectangle. Show your work. a) cm The area of a rectangle, when viewed on a grid, is like a multiplication array. cm cm x cm = cm cm b) cm. Calculate the area of each rectangle. Use the rule for area of a rectangle. Show your work. a) b) m cm x cm = cm cm cm For example, this rectangle has a width of cm and a length of cm. The area of the rectangle can be found by multiplying the length by the width. cm cm cm The general rule for the area of a rectangle is area length width m cm x cm = cm m x m = m. Nancy is using cm tiles to make rectangular coasters. Each tile costs \$.. Which coaster will cost the most? Explain. cm cm cm cm cm cm by cm rectangle. This shape has the greatest area ( cm ). Answers Chapter : Area and Grids Copyright by Thomson Nelson

5 -NEM-WBAns-CH // : PM Page Solve Problems by Solving Simpler Problems Solve problems by breaking them into smaller parts.. Alain s parents are purchasing new flooring for their living room. The flooring costs \$/m. How much will the flooring cost before taxes? m The area of a complex shape can sometimes be found by dividing it into several smaller parts. The total area is then equal to the sum of the areas of the smaller parts. m m m Scale cm = m a) Calculate the area by dividing the shape into two parts. Use different sets of rectangles. Did you get the same answer? Explain why or why not. m. The area was the same for both sets of For example, the area of this shape can be calculated two ways. area area of cm by cm square area of cm by cm rectangle cm rectangles because the overall shape of the room did not change, only the way it was divided. b) Calculate the cost of the flooring.. A photograph is cm by cm. It has a mount that is cm wide all around it. What is the area of the mount? Show your work. cm cm cm cm cm cm \$ or area area of cm by cm rectangle area of cm by cm rectangle cm (area of photo and mount) cm x cm = 9 cm (area of photo) cm x cm = 9 cm (area of mount) 9 cm - 9 cm = cm Copyright by Thomson Nelson Answers Chapter : Area and Grids

6 -NEM-WBAns-CH // : PM Page Modelling Area Model area using an appropriate scale.. Jasleen s parents are planning a community garden. The dimensions are m by m. They want to make a scale model of the garden on centimetre grid paper. a) Choose an appropriate scale. Explain your choice. Suggested scale: cm = m Using this scale, the garden can easily fit on the grid. The model of the garden will be cm by cm. b) Model the garden. Include the scale. Suggested model: Large objects, such as floor plans, towns, and buildings, can be modelled using a scale. A scale model may be larger or smaller than the real object but must be the same shape. A scale model is similar to the real object. When choosing a scale, consider the size of the object and the space you have available for the model. For example, to draw a model of a m by m patio on the grid below, an appropriate scale would be cm m. The model will then be cm ( ) by cm ( ). m m m Scale cm = m c) What is the area of the garden? Include the units. m m Scale cm = m Remember to always include the scale on your model. d) What is the area of the model? Include the units. (using suggested model) cm. Would you measure each area in square kilometres, square metres, square centimetres, or square millimetres? a) a restaurant b) a function key on a calculator c) a country d) a postcard square metres square millimetres or square centimetres square kilometres square centimetres Answers Chapter : Area and Grids Copyright by Thomson Nelson

7 -NEM-WBAns-CH // : PM Page Coordinate Grids Use coordinate pairs to identify and describe locations on a grid.. Ari drew this logo on a coordinate grid. 9 9 a) What points on the grid could you use to describe the logo? Write the coordinates for each point. (, ), (, ), (, ), (, ), (, ), (, ), and (9, ) b) Write instructions for drawing the logo from these points. Plot the points in Part a), then join the points A coordinate grid is a grid with each horizontal and vertical line numbered in order. Coordinates identify locations on a coordinate grid, and are sets of numbers that describe where a vertical and a horizontal line meet. The coordinate from the horizontal axis is always written first. For example, the vertices of the triangle below have coordinates (, ), (, ), and (, ). 9 vertical axis 9 horizontal axis with straight lines to form a closed polygon.. Ken started drawing the initial of his first name on a coordinate grid. a) Name the coordinates he has used so far. (, ), (, 9), and (, 9) b) Write the coordinates he would need to finish the letter K. Mark these points on the grid and finish the initial. Suggested answer: (, ) and (, ) 9 9 Copyright by Thomson Nelson Answers Chapter : Area and Grids

8 -NEM-WBAns-CH // : PM Page Test Yourself Circle the correct answer.. What is the area of each shape in square units? A. square units, square units B. square units, square units C. square units, square units D. 9 square units,. square units. What is the area of each shape to the nearest square centimetre? A. cm, cm B. cm, cm C. cm, cm D. cm, cm. Pat made a rectangle using square stickers. The stickers are cm. The perimeter of the rectangle is cm. Of all the rectangles Pat could have made, what are the dimensions of the rectangle with the smallest area and the rectangle with the largest area? A. cm by 9 cm, cm by cm B. cm by cm, cm by cm C. cm by cm, cm by cm D. cm by cm, cm by cm. A rectangle has an area of cm. What dimensions would give the shortest perimeter? A. cm by cm B. cm by cm C. cm by cm D. cm by cm Answers Chapter : Area and Grids Copyright by Thomson Nelson

9 -NEM-WBAns-CH // : PM Page 9 Test Yourself Page. What is the area of each rectangle? km m m 9 km A. cm, cm B. m, km C. cm, cm D. m, km. A zoo has the shape of an km by km rectangle. A scale model of the zoo is shown below. What are the areas of the zoo and the model? A. km, cm B. km, cm km C. km, cm D. km, cm km Scale cm = km. What coordinates would describe this shape? A. (, ), (, ), (, ), (, ), (, ), and (, ) B. (, ), (, ), (, ), (, ), (, ), and (, ) C. (, ), (, ), (, ), (, ), (, ), and (, ) D. (, ), (, ), (, ), (, ), (, ) and (, ) 9 9 Copyright by Thomson Nelson Answers Chapter : Area and Grids 9

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