Math – More Area Lesson 5 – Nov 13

Review – what did we cover yesterday? Area of Rectangle = Length X Width OR Base X Height. Area of Parallelogram = Base X Height. Are they related? YES …. The Polygon family! How? A rectangle can change into a parallelogram and vice-versa (parallelogram into a rectangle) WITHOUT changing the area. What’s the difference then in getting the area of rectangle versus the area of parallelogram? It is just one extra step in knowing the height (not the width) of the parallelogram first before getting its area. Base (or Length) Height (or Width) Base (or Length) Width Height Height: the distance between one side of the parallelogram and the opposite side. It is measured along a line that is perpendicular to the base.

Who else can be in the Polygon family? Rectangle. Square. Parallelogram. Triangle. Anything with a side!

Polygon family – Relation Your task! So we looked at how parallelograms and rectangles are related. What about the relation between rectangles and triangles OR between parallelogram and triangles? Hint: – Draw a rectangle. Then using one line, show me how it can be changed into 2 equal triangles! – Draw a parallelogram. Then using one line, show me how it can be changed into 2 equal triangles! – Figure out the area of the triangle.

So what did you find? What do you think the area of a triangle is then? Area of rectangle: Base X Height OR Length X Width Area of parallelogram: Base X Height Area of triangle: (Base X Height) Base Height 2

Now that you know the area of a rectangle, a parallelogram, and a triangle, figure out the following: Ms. Abulnour’s living room is not a rectangle and it is not a parallelogram. Actually it is this shape! She does not know how to get the area of her living room. How can she get the area of her living room then to fit the boxes of books she has? Hint: Remember that the area is seeing how much space you have INSIDE your shape. So there is a way to figure out the area! 8 m 20 m 7 m 8 m 7 m 8 m Questions: (show your work) 1)Find the perimeter of the shape (use the three steps). 2)Find the area of the shape (show your work). 3)If each box of books equals 5 m 2, then how many boxes fit the living room? 4)If each box of books equals 6 m 2, then how many boxes fit the living room now? 6 m 7 m 5 m 6 m 5 m

Questions: 2) Find the perimeter of the shape (use the three steps). Perimeter = Side 1 + Side 2 + Side 3 + Side 4 + Side 5 + Side 6 + Side 7 + Side 8 + Side 9 = 20 m + 8 m + 8 m + 7 m + 8 m + 7 m + 6 m + 6 m + 8 m = 78 m.

Question: 3) Find the area of the shape (show your work). To get the area of the whole shape: 1)Divide the whole shape into pieces of polygons (so anything from a square, rectangle, triangle, and parallelogram). So we can divide the shape into one rectangle, one parallelogram, and one triangle. Area 1: Rectangle 1: Base X Height = 20 m X 8 m = 160 m 2 Adding all 4 areas to get the area of the whole shape: Area of Ms. Abulnour’s living room = Area 1 + Area 2 + Area 3 = Area 2: Parallelogram 1: Base X Height = 7 m X 5 m = 35 m 2 Area 3: Triangle 1: (Base X Height) divided by 2 = 6 m X 5 m = 30 m 2 2) Once divided into its pieces of polygons, get the area of each piece of polygon: We have one rectangle, one parallelogram, and one triangle, so we have 3 things to get the area of: 160 m m m 2 =225 m 2

Questions: 4) If each box of books equals 5 m 2, then how many boxes fit the living room? I now know that the area of Ms. Abulnour’s living room is 225 m 2, so if each box equals 5 m 2, then: = 225m 2 = 45 boxes. 5 m 2

Questions: 5) If each box of books equals 6 m 2, then how many boxes fit the living room? I now know that the area of Ms. Abulnour’s living room is 225 m 2, so if each box equals 6 m 2, then: = 225m 2 = 37.5 boxes = 37 boxes (I can’t have 37.5 boxes). 6 m 2

Got it? Any questions?