© 2007 m. tallman. the area of this rectangle is 40 cm². if you divide this rectangle in half,...
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![Page 1: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/1.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
![Page 2: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/2.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
The area of this rectangle is 40 cm².
If you divide this rectangle in half, what two shapes do you see?
A = 40 cm²
![Page 3: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/3.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
The area of this rectangle is 40 cm².
If you divide this rectangle in half, what two shapes do you see?
Triangles
So if the rectangle’s area is 40 cm², what is ½ of the rectangle’s area?
20 cm²
A = 20 cm²
A = 40 cm²
![Page 4: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/4.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
The area of this parallelogram is 64 cm².
If you divide this parallelogram in half, what two shapes do you see?
A = 64 cm²
![Page 5: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/5.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
The area of this parallelogram is 64 cm².
If you divide this parallelogram in half, what two shapes do you see?
Triangles
So if the parallelogram’s area is 64 cm², what is ½ of the parallelogram’s area?
32 cm²
A = 32 cm²
A = 64 cm²
![Page 6: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/6.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
Since triangles are ½ of a rectangle or parallelogram, the formula for finding the area of
triangles is A = ½bh.
A = 8 cm × 5 cmA = 40 cm²
A = 8 cm × 5 cm
A = 20 cm²
½ ×A = 4 cm × 5 cm
![Page 7: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/7.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
Since triangles are ½ of a rectangle or parallelogram, the formula for finding the area of
triangles is A = ½bh.
A = 8 cm × 8 cmA = 64 cm²
A = 8 cm × 8 cm
A = 32 cm²
½ ×A = 4 cm × 8 cm
![Page 8: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/8.jpg)
© 2007 M. Tallman
If you know the base (b) and the height (h) of a triangle, you can use a formula to find its area.
If you multiply the ½ × b × h, you get the area (A).
A = ½ × b × h
or
A = ½bh
A = 6 cm × 3 cm
A = 9 cm²
½
×A = 3 cm × 3 cm
A = 4 cm × 5 cm
A =10cm²
½
×A = 2 cm × 5 cm
A = 6 cm × 7 cm
A = 21 cm²
½
×A = 3 cm × 7 cm
![Page 9: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/9.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
The way the factors are grouped does not change the product.
The associative property can make finding the area of a triangle easier!
= 24 = 24 33 22xxxx44(( ))
(4 × 3) × 2=4 × (3 × 2)
![Page 10: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/10.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
(½ × h) × b
½½ bb(( ))AA == ×× ×× hh
(½ × b) × h=½ × (b × h)=Group the factors in which ever way
that makes the problem easier to solve.
The way the factors are grouped does not change the product.
The associative property can make finding the area of a triangle easier!
![Page 11: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/11.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
Use the formula A = ½bh to find the area of the triangle.
8 ft
A = 8 ft) × 9 ft
A = 36 ft²
9 ft
(½ ×
A = 4 ft × 9 ft
![Page 12: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/12.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
Use the formula A = ½bh to find the area of the triangle.
20 yd
A = 20 yd)× 14 yd
A = 140 yd²
14 yd
(½ ×A = 10 yd × 14 yd
![Page 13: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/13.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
Use the formula A = ½bh to find the area of the triangle.
16 m
A = 16 m) × 9 m
A = 72 m²
9 m
(½ ×A = 8 m × 9 m
![Page 14: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/14.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
Use the formula A = ½bh to find the area of the triangle.
7 in
A = 7 in × 10 in
A = 35 in²
10 in
½ ×A = 7 in × 5 in
![Page 15: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/15.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
Use the formula A = ½bh to find the area of the triangle.
11 mm
A = (11 mm×6 mm)
A = 33 mm²
6 mm
½ ×A = 11 mm × 6 mm
![Page 16: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/16.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
A =36units²
![Page 17: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/17.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
A =27.5units²
![Page 18: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/18.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
A =24units²
![Page 19: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/19.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
A =20units²
![Page 20: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/20.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
A = 9 units²
![Page 21: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/21.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
A =16units²
![Page 22: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/22.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
A =21units²
![Page 23: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/23.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
6 mm
8 mm
b
A = 24 mm²
24 mm² × =2 48 mm²
48 mm² ÷ 8 mm = 6 mm
![Page 24: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/24.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
8.5 fth
14 ft
A = 59.5 ft²
59.5 ft² × =2 119 ft²
119 ft² ÷ 14 ft = 8.5 ft
![Page 25: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/25.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
12 inb
9 in
A = 54 in²
54 in² × =2 108 in²
108 in² ÷ 9 in = 12 in
![Page 26: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/26.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
11.5 ft
7 ft
h
A = 40.25 ft²
40.25 ft² × =2 80.5 ft²
80.5 ft² ÷ 7 ft = 11.5 ft
![Page 27: © 2007 M. Tallman. The area of this rectangle is 40 cm². If you divide this rectangle in half, what two shapes do you see? A = 40 cm²](https://reader033.vdocuments.net/reader033/viewer/2022061305/551444d6550346414e8b4b44/html5/thumbnails/27.jpg)
© 2007 M. Tallman
© 2007 M. Tallman
8 ydb
A = 48 yd²
48 yd² × =2 96 yd²
96 yd² ÷ 12 yd= 8 yd
12 yd