1. 2D Perimeter and Area

2. Objectives
Find the area and perimeter of quadrilaterals(四边形) and triangles
Find the area(面积) and perimeter(周长)of complex shapes (复杂的形) formed from quadrilaterals and triangles
Find the area, radius(半径) , diameter(直径) and circumference(圆周) of circles.
Find the area of complex shapes involving circles and half circles.
Find measurements for arcs(弧) and sectors(扇形).
Find the area of complex shapes involving arcs and sectors.

3. Purposeful mistakes
In the following questions about perimeter and area I have intentionally made mistakes in my answer. It’s your mission to solve the problems and determine my mistakes.

4. Rectangles have length and width.
Quadrilaterials
Rectangles have length and width.
What do the b and the h mean?

5. Quadrilaterials
Name the length, width, base and height and then solve for the area and perimeter of these two shapes.

6. Quadrilaterials Length = 12.6cm Width = 6.4cm Area = 38cm
Perimeter = 80.64cm2
Base = 2.5m
Height = 1.8m
Area = 4.5m2
Perimeter = 9m2

7. Quadrilaterials

8. Quadrilaterials
Name the base and height and then solve for the area and perimeter of these two shapes.

9. Quadrilaterials
Name the base and height and then solve for the area and perimeter of these two shapes.
Base = 18mm
Height = 11mm
Area = 213m2
Perimeter = 57mm
Base = 5m
Height = 5cm
Area = 20cm2
Perimeter = 20cm

10. Triangles
Name the base and height and then solve for the area and perimeter of this shape.

11. Triangles Base = 17in Height = 13in Area = 110.5in2 Perimeter = 47in
Name the base and height and then solve for the area and perimeter of this shape.

12. Circles

13. Circles For each of these give
the radius, diameter and find the area and circumference.

14. Circles Radius: 2cm Diameter: 4cm Area: 4∏cm2 Circumference: 4∏cm
Radius: 15ft
Diameter: 30ft2
Area: 225∏ ft2 Circumference: 30∏

15. Circles
A circle is 360o degrees around. The symbol o stands for degrees.
If the circle to the right has a diameter of 60cm2 and the value of theta (ϴ) is 100o then what is the area of the sector?

16. Circles Solution Area of a sector = πr2 x (ϴ / 360)
A = 900 π x (100/360)
A = 900 π x (5 / 18)
A = 250 π or about 785.4
A sector is a part of a circle.

17. Missing variables word problems
To solve these problems draw a picture and label the missing parts.
If a triangle has an area of 50cm2 with a height of 12cm then what is the base?
If a trapezoid has a base of 30cm, height of 12 cm, and area of 800cm2 then what is the top?
If a circle has an area of 85cm2 then what is the diameter?

18. Missing variables word problems
To solve these problems draw a picture and label the missing parts.
If a triangle has an area of 50cm2 with a height of 12cm then what is the base? 8.33cm
If a trapezoid has a base of 30cm, height of 12 cm, and area of 800cm2 then what is the top?
If a circle has an area of 85cm2 then what is the diameter? r = 5.2 so d = 10.4
Why aren’t these answers the best possible answer?

19. Word problems involving circles
A circle has two minor sectors which are opposite of each other and each span an angle of 45o. If the circle has a diameter of 30mm, then what is the area of the sectors?
A family owns a piece of land which is 12000m2. On the land they put a house which is 30m by 55m, a circular swimming pool which is 10m in diameter, and a driveway that is 5m wide and 40m long. They want to buy some horses. If each horse needs 300m2 then how many horses can the have?

20. Word problems involving circles
A circle has two minor sectors which are opposite of each other and each span an angle of 45o. If the circle has a diameter of 30mm, when what is the area of the sectors? 56.25π or
A family owns a piece of land which is 12000m2. On the land they put a house which is 30m by 55m, a circular swimming pool which is 10m in diameter, and a driveway that is 5m wide and 40m long. They want to buy some horses. If each horse needs 300m2 then how many horse can the have? 33 horses.

21. You now have all the tools you need to solve more complex problems.
What is the area of the shape on the left and the blue part of the shape on the right?