Transcript Perimeter, Area and Volume

Perimeter, Area and Volume
Perimeter
Perimeter is the distance around the outside
of a figure.
(think putting a fence up around your yard)
To calculate perimeter: add up all the sides
of a figure.
Perimeter
Add up all the sides of a shape.
12cm
6cm
6cm
8cm
6cm
12 + 8 + 12 + 8 = 40cm
6 + 6 + 6 = 18cm
Right Triangles
• There is a specific formula used to figure
out the lengths of sides in a right triangle
(a triangle containing a right angle).
• The side opposite the right angle is called
the hypotenuse (and is indicated by “c” in
the formula)
Circumference
• Circumference is the word used to describe the perimeter of a circle,
or the distance around the entire circle.
• Radius is defined as the distance from the center of the circle to any
point on the perimeter of the circle.
• Diameter is defined as the distance that connects 2 points on the
circle and passes through the center of the circle
Circumference
• C=π2r or C=πd
Area
Area is a measure of the amount of space
inside an figure’s base, or the amount of
square units in a figure :
(think coverage of a carpet).
There are different formula that you need to
learn for different shapes.
Area is measured in square units :
( sq. units or units2 ) .
Area
• Triangle
• Area =( base x height ) ÷ 2
• 10 x 12 = 120
• 120 ÷ 2 = 60
• Answer : 60 cm²
12cm
10cm
Area
11cm
8cm
8cm
8cm
Square and Rectangle
Area = length x width
11 x 8 = 88
8 x 8 = 64
Answer : 88 cm²
Answer : 64 cm²
Area
Parallelogram
12cm
Area = base x perpendicular height
15cm
15 x 12 = 180
Answer : 180cm²
Area
b
h
Trapezoid
Area = ½ x h x ( b1 + b2 )
b
10cm
½ ( 10 + 12 ) x 5
11 x 5 = 55
5cm
12cm
Answer : 55cm²
Area
Circle
A=πr2
or
A=π(d/2)2
Volume
Volume is a measure of a 3-dimensional figure’s capacity.
(think amount of water that can fit inside a fish tank)
Volume is measured in units cubed (units3).
PRISMS
Prisms are
Volume
Cube and Rectangular Prism
4cm
5cm
5cm
2cm
5cm
5cm
Volume = Area (of base) x height
Volume = length x width x height
5 x 5 x 5 = 125
5 x 2 x 4 = 40
Answer : 125cm³
Answer : 40cm³
Volume
Triangular Prism
Volume = Area (of triangle) x height
Volume = ½ (base x height) x height
7cm
10cm
5cm
½ x ( 5 x 7 ) x 10 = 175
Answer : 175 cm³
Volume
Cylinder
Volume = Area (of circle) x h
Height =
10cm
Volume = π x r² x h
π x 5² x 10
π x 5 x 5 x 10 = 785
Answer : 785cm³
Radius =
5cm
Pyramids and and Cones
Pyramids and Cones are different from prisms because they each
A pyramid has a square or rectangular base
A cone has a circular base
Volume
Pyramid
(square or rectangular base)
Volume =
Cone
(circular base)
Volume =