Calculating perimeter, area, surface area, and volume : Calculating perimeter, area, surface area, and volume Geometry – 7 th Grade Ms. Cuautle
Objective : Objective You will learn to use formulas routinely for finding the perimeter and area of two-dimensional figures and the surface area and volume of three-dimensional figures Before we get started think… What is a two-dimensional and three-dimensional figure? What are some components of these two different figures we would like to evaluate?
A two-dimensional vs. three dimensional figure: A two-dimensional vs. three dimensional figure What is a two dimensional figure? A 2-D figure contains only a base and height. It is a figure that is flat What is a three dimensional figure? A 3-D figure contains height, width, and depth. It is a figure that contains space inside. Watch this video of 2-D and 3-D shapes
Perimeter and Area : Perimeter and Area What is perimeter? Perimeter is the total distance around the border of a closed two-dimensional figure. It is measured in linear units such as inches, feet, or meters. Note: The perimeter of a circle is called the circumference. Think: How are perimeter and area related to each other? How can you incorporate perimeter and area to three-dimensional figures? What is area? Area is the amount of space inside the boundary of a closed two-dimensional figure. It is measured in square units such as square inches or square feet. Fun video of Perimeter and Area
Perimeter formulas : Perimeter formulas
Area formulas : Area formulas
Examples for calculating perimeter: Examples for calculating perimeter Calculate the perimeter. 1) Add all of the sides P = 7 + 4 +7 + 4 P = 22 in. 2) Use the formula of diameter for rectangles P = 2b + 2h P = 2(7) + 2(4) P = 14 +8 P = 22 in. Calculate the circumference. Use the formula of circumference for circles. P = π d P = π P ≈ 56.55 in. Think: When the diameter is given, how can you find what the radius is?
Examples for calculating area : Examples for calculating area Use the formula of area for trapezoids. A= A = ½ (3 + 11) x 7 A = ½ (14) x 7 A = 7 x 7 A= 49 cm. Calculate the area. Use the formula of area for triangles. A = ½ b h A = ½ (3) (3) A = ½ (9) A = 4.5 cm. Calculate the area. (cm) Think: How can you determine which base to use for
Surface Area and Volume : Surface Area and Volume What is surface area? Surface area is the total area of the surface of a three-dimensional figure. It is the sum of all of the areas of the shapes that cover the surface. It is measured in square units such as square inches or square feet. What is volume? Volume is the measure of the amount of space inside of a solid figure. It is measured in cubic measurements such as cubic feet or cubic centimeters. Think: How are surface area and volume related to each other? Can surface area and volume be used in 2-dimensional figures?
Surface area formulas : Surface area formulas
Volume formulas : Volume formulas
Examples for calculating surface area: Examples for calculating surface area Calculate the surface area. Use the formula of surface area for rectangular prisms. A = 2 lw + 2 lh + 2 wh A = 2 (5) (4) + 2 (5) (7) + 2 (4) (7) A= 2 (20) + 2 (35) + 2 (28) A= 40 + 70 + 56 A = 166 Calculate the surface area. Use the formula of surface area for spheres. A = A = A = 4 (81) A = 324 A Think: When multiplying length, width, and height, does order matter?
Examples for calculating volume: Examples for calculating volume Calculate the volume. Use the formula of volume for rectangular prisms V = lwh V= (5) (4) (7) V = 20 (7) V = 140 Calculate the volume. Use the formula of volume for cylinders. V = V = V= V= V