2D Perimeter and Area
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.
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.
Quadrilaterials
Rectangles have
length and width.
What do the b
and the h mean?
Quadrilaterials
Name the length, width, base
and height and then solve for
the area and perimeter of these
two shapes.
Quadrilaterials
Length = 12.6cm
Width = 6.4cm
Area = 38cm
Perimeter = 80.64cm2
Base = 2.5m
Height = 1.8m
Area = 4.5m2
Perimeter = 9m2
Quadrilaterials
Quadrilaterials
Name the base and height and
then solve for the area and
perimeter of these two shapes.
Quadrilaterials
Name the base and height and
then solve for the area and
perimeter of these two shapes.
Base = 5m
Height = 5cm
Area = 20cm2
Perimeter = 20cm
Base = 18mm
Height = 11mm
Area = 213m2
Perimeter = 57mm
Triangles
Name the base and height and
then solve for the area and
perimeter of this shape.
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.
Circles
Circles
For each of these give
the radius, diameter
and find the area and
circumference.
Circles
Radius: 2cm
Diameter: 4cm
Area: 4∏cm2
Circumference: 4∏cm
Radius: 15ft
Diameter: 30ft2
Area: 225∏ ft2
Circumference: 30∏
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?
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.
Missing variables word problems
To solve these problems draw a picture and label the missing parts.
1) If a triangle has an area of 50cm2 with a height of 12cm then
what is the base?
2) If a trapezoid has a base of 30cm, height of 12 cm, and area of
800cm2 then what is the top?
3) If a circle has an area of 85cm2 then what is the diameter?
Missing variables word problems
To solve these problems draw a picture and label the missing parts.
1) If a triangle has an area of 50cm2 with a height of 12cm then what
is the base? 8.33cm
2) If a trapezoid has a base of 30cm, height of 12 cm, and area of
800cm2 then what is the top? 103.33
3) 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?
Word problems involving circles
1. 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?
2. 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?
Word problems involving circles
1. 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 176.71
2. 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.
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?