Unit 7: Geometry - Area, Surface Area & Volume
Master geometry by solving real-world problems involving area, surface area, and volume of 2D and 3D shapes
Unit 7 Overview
Unit 7 focuses on geometry, specifically solving real-world and mathematical problems involving area, surface area, and volume. Students extend their understanding of area from rectangles to more complex figures like triangles, quadrilaterals, and polygons, and apply area, surface area, and volume formulas to solve practical problems.
You'll learn to calculate areas of triangles, quadrilaterals, and polygons, find areas of composite figures, understand surface area using nets, calculate volumes of rectangular prisms, and apply these concepts to real-world problems. This unit helps build a foundation for high school geometry by improving spatial reasoning and formula fluency.
Get ready to become a geometry master!
Learning Objectives
- Calculate the area of triangles, quadrilaterals, and polygons using appropriate formulas
- Find the area of composite figures by decomposing them into familiar shapes
- Use nets to understand and calculate surface area of 3D figures
- Calculate volume of right rectangular prisms using the formula V = l Γ w Γ h
- Apply area, surface area, and volume concepts to solve real-world problems
- Develop spatial reasoning skills and formula fluency for geometry
Your Progress
Area of Triangles, Quadrilaterals, and Polygons
Students learn to find the area of two-dimensional figures by decomposing them into familiar shapes (like triangles and rectangles) and using known formulas. They explore how area applies to real-world tasks, such as designing spaces or estimating coverage.
This section covers triangles, quadrilaterals, and polygons, teaching students to break down complex shapes into simpler components and apply the appropriate area formulas.
What You'll Learn:
- Calculate area of triangles using A = (base Γ height) / 2
- Find area of quadrilaterals (rectangles, squares, parallelograms, trapezoids)
- Decompose polygons into familiar shapes to find area
- Apply area concepts to real-world design and estimation problems
Key Formulas:
- Triangle: A = (base Γ height) / 2
- Rectangle/Square: A = length Γ width
- Parallelogram: A = base Γ height
- Trapezoid: A = (base1 + base2) / 2 Γ height
Why it matters: essential for designing spaces, calculating materials needed, and solving real-world geometry problems.
Math Antics β Area of Triangles
Explains the triangle area formula with clear visuals and step-by-step examples to help you master triangle area calculations.
Watch on YouTubeMath Antics β Area of Polygons
Shows how to break complex shapes into simpler parts and calculate their areas using the appropriate formulas.
Watch on YouTubeArea of Composite Figures
Composite figures are made up of multiple simple shapes. Students learn to divide these shapes, calculate individual areas, and add or subtract them to find the total.
This section teaches students to break down complex shapes into familiar components like rectangles, triangles, and other polygons, then calculate the total area by adding or subtracting individual areas.
What You'll Learn:
- Identify simple shapes within composite figures
- Calculate the area of each component shape
- Add or subtract areas to find the total area
- Apply this method to real-world composite shapes
Finding Area of Composite Figures (Math with Mr. J)
Step-by-step breakdown with examples showing how to find the area of composite figures by breaking them into simple shapes.
Watch on YouTubeKhan Academy β Area of Composite Shapes
Demonstrates splitting complex figures into simple shapes, calculating each area, then adding to get the total.
Watch on YouTubeSurface Area of 3D Figures (Nets)
Students use nets (unfolded 3D shapes) to understand and calculate surface area. They focus on rectangular prisms, triangular prisms, and pyramids, applying formulas or adding up the areas of each face.
This section teaches students to visualize 3D shapes as 2D nets, calculate the area of each face, and find the total surface area by adding all face areas together.
What You'll Learn:
- Understand what nets are and how they represent 3D shapes
- Calculate the area of each face in a net
- Add all face areas to find total surface area
- Apply this method to prisms, pyramids, and other 3D shapes
Khan Academy β Surface Area
Learn how to calculate surface area using nets with clear explanations and step-by-step examples.
Watch on YouTubeFinding Surface Area Using Nets (Mr. J)
Shows how to label and add all face areas to find the total surface area of 3D shapes using nets.
Watch on YouTubeVolume of Right Rectangular Prisms
Volume is the amount of space inside a 3D object. Students learn to apply the formula V = l Γ w Γ h and also understand volume through counting unit cubes.
This section focuses on rectangular prisms, teaching students to calculate volume using the length Γ width Γ height formula and understand volume as the space occupied by a 3D shape.
What You'll Learn:
- Apply the volume formula V = l Γ w Γ h for rectangular prisms
- Understand volume through counting unit cubes
- Calculate volume with fractional dimensions
- Apply volume concepts to real-world problems
Khan Academy β Volume of Rectangular Prisms
Introduces volume with visual models and explains how to calculate volume of rectangular prisms with clear examples.
Watch on YouTubeMath with Mr. J β Volume
Explains the volume formula and provides step-by-step examples to help you master volume calculations.
Watch on YouTubeReal-World Geometry Problems
Students apply their understanding of area, surface area, and volume to solve real-world problemsβlike designing a garden, wrapping a gift, or building a box. This brings meaning and application to the abstract math skills they've learned.
This section connects geometry concepts to practical situations, helping students see how mathematical formulas apply to everyday problems and real-world scenarios.
What You'll Learn:
- Apply area formulas to real-world design problems
- Use surface area calculations for wrapping and covering
- Apply volume concepts to capacity and space problems
- Solve multi-step geometry problems with real-world context
Volume Word Problems (Khan Academy)
Real-world applications of volume with practical examples showing how to solve volume problems in context.
Watch on YouTubeArea & Perimeter Word Problems (MashUp Math)
Applies area concepts to real-life situations with practical examples and step-by-step solutions.
Watch on YouTubeSummarizing & Comparing Data Sets
Summarizing data involves reporting the number of observations, describing the attribute and its units, and giving quantitative measures of center (mean or median) and variability (range or IQR).
Students learn to choose appropriate graphs (dot plots, histograms, box plots) and decide whether the mean or median better describes a distribution based on its shape. The essential questions encourage students to compare data sets, decide which graphs best represent data and draw conclusions.
What You'll Learn:
- Summarize data sets using appropriate measures
- Choose the best graph type for different data
- Compare multiple data sets effectively
- Draw meaningful conclusions from data analysis
Khan Academy β Comparing Dot Plots, Histograms & Box Plots
Learn how to compare different data displays and choose the most appropriate graph for your data.
Watch on YouTubeKhan Academy β Impact on Mean & Median When Removing Data
Understand how removing data points affects the mean and median, and learn to choose the best measure of center.
Watch on YouTube