Perimeter & Area 5.1

1. Perimeter & Area 5.1

2. Define perimeter and area. • Apply the area and formula of a rectangle and triangle. • Find the perimeter of a figure. • Use two methods to find the area of compound figures. • Approximate the area of an irregular figure. • Apply area to real world situations.

3. Area • The number of square units needed to cover the region inside a figure. • Area is always measured in square units! There are 40 squares covering the inside of the figure.

4. Area • To calculate the area of a rectangle use the formula: Area = Length x Width Area = 9m x 2mArea = 18 square meters

5. Area • To calculate the area of a triangle use the formula: Area = ½Base x Height

6. Start at one of the vertices and sum the numbers clockwise or counterclockwise. Start Perimeter • The perimeter is the distance around a figure. 10 + 6 + 4 + 10 + 10 + 6 + 4 + 10 = 60 m

7. Find the Area & Perimeter 5 inches Perimeter = 20 inches 3 inches Area = 9 inches² a. b. c. perimeter 16 cm perimeter 12 in perimeter 20 cm about 7 cm2 area 5 in2 about 9 cm2

8. This side was 8m but because you split it to make two regular rectangles, look carefully at every side of the figure to see what the new measurements will be! Don’t forget the rule, opposite sides are equal! This will help you find the missing measurements! Find the Area Find the area of rectangle “B”A= L x W A = 10m x 4m A = 40 square m Find the area of rectangle “A”A= L x W A = 4m x 4m A = 16 square m 40 square m + 16 square m56 square m The total area is 56 square m.

9. A shape that is made from other shapes is known as a composite shape. To find the area of this shape we have to split it up into two rectangles. Area 4cm 2cm 4cm Area = 4 x 10 10cm Area = 4 x 8 8cm 40cm2 32cm2 8cm Total area = 40 + 32 = 72 cm2

10. Area & Perimeter 5cm 2cm Area = 4 x 5 Area = 5 x 9 4cm 9cm 5cm 20cm2 45cm2 4cm 2cm Total area = 45 + 20 = 65 cm2 Perimeter = 36 cm 5cm

11. 2cm 5cm 11cm 4cm 6cm 6cm Area & Perimeter Total area = 10 + 36 = 46 cm2 Perimeter = 34 cm Area = 2 x 5 Area = 6 x 6 10cm2 36cm2

12. There is another way of doing this question. Area = 4 x 7 Area = 4 x 4 28cm2 16cm2 4cm 3cm Area = 3 x 7 3cm 3cm 4cm 21cm2 7cm 7cm Total area = 28 + 16 + 21 = 65 cm2 Perimeter = 42 cm 11cm

13. Lost Area Method Area = 3 x 4 12cm2 4cm 3cm 3cm 3cm 4cm 7cm 7cm Area = 7 x 11 77cm2 Total area = 77 – 12 = 65 cm2 Perimeter = 42 cm

14. 5cm 2cm 4cm 9cm 5cm 4cm 2cm 5cm Find the area using composition of area method A = 5 x 9 + 5 x 4 A = 45 + 20 A = 65 cm2

15. 2cm 5cm 11cm 4cm 6cm 6cm Find the area using the lost area method A = 6 x 11 – 5 x 4 A = 66 – 20 A = 46 cm2

16. Find the area of the figure. Total area = 16(14) – 60 –60= 104 m2

17. Find the area of the figure. Total area= 3,560 square ft.

18. Answer the following question. Mike is remodeling his kitchen. The countertop he wants costs $2.70 per square foot. How much will Mike have to spend on his remodeling project? Total area = 12 + 12 = 24 ft2 Price per square foot $2.70 2.70 x 24 $64.80

19. Approximate Area of an Irregular Figure There are 8 squares completely inside the figure (X) and 12 partly inside the figure (•).

20. Count the complete squares.     X X  Count the partial squares.  X X   Approximate Area of an Irregular Figure

21. Estimate the shaded area. The grid has squares with side lengths of 1 cm. about 7 cm2 about 7.5 cm2 a. b.

22. Estimate the shaded area. The grid has squares with side lengths of 1 cm. about 10.5 cm2 a.

23. Add the area of the rectangle to the area of the two triangles. Find the area of the composite figure that is made up of known shapes A = l x w A = 6 x 5 A = 30 units2 Total Area = 30 + 2.5 + 9 Total Area = 41.5 units2

24. 4cm 4cm 2cm 8cm 4cm 6cm Find the area. about 24 cm2 about 40 cm2 a. b.

25. Answer each of the following questions. 15 x 20 = 300 square units 2(15) + 2(20) = 70 units 3 x 20 = 60 square units 2(3) + (2)20 = 46 units 8 x 13 = 104 square units

26. Assignment 5.1A 1 - 8 and 5.1B 1 - 10 Day 2 Basic Area 1 – 29