Unit 5: Geometry โ Area & Volume
Explore the fascinating world of geometry, mastering area, surface area, and volume calculations while solving real-world problems with visual models
Unit 5 Overview
This is another math-packed unit on the concept of area and volume and how using them, we can help measure spaces and objects. We will find ways of determining the area of certain specific shapes, such as a triangle and polygons, either by breaking them down into simpler shapes or by finding new ways of measuring them.
Volume measurements tell us how much space an object takes up. You're going to use cool tools and strategies to solve real-world problems involving area problems of things such as the area of a room or volume of boxes. Plus, you'll be using drawings and models to help us see the solutions.
Get ready to see your space in a new way!
Learning Objectives
- Calculate area of rectangles, squares, triangles, parallelograms, and trapezoids
- Decompose composite shapes and compute total area
- Use nets to find surface area of prisms and pyramids
- Compute volume of rectangular prisms, including fractional edges
- Compare and choose between surface area and volume in real contexts
Your Progress
Understanding Area of Polygons
Area is the amount of space inside a two-dimensional shape. It is measured in square units.
Polygons covered: rectangles, squares, triangles, parallelograms, trapezoids.
What You'll Learn:
- Calculate area of rectangles, squares, triangles, parallelograms, and trapezoids
- Apply the correct formula for each polygon type
- Understand the relationship between base, height, and area
- Solve real-world problems involving area calculations
Formulas:
- Rectangles and Squares: A = length ร width
- Triangles: A = (base ร height) / 2
- Parallelograms: A = base ร height
- Trapezoids: A = (base1 + base2) / 2 ร height
Why it matters: planning flooring, painting, or designing spaces.
Math Antics โ Introduction to Area
Introduces the concept of area and demonstrates formulas for common polygons like rectangles, triangles, and parallelograms with clear visuals.
Watch on YouTubeKhan Academy โ Area of a Parallelogram
Shows how the area of a parallelogram relates to a rectangle and how to use base and height to compute area.
Watch on YouTubeCalculating Area of Composite Shapes
Break the shape into simpler shapes, find each area, and add them together.
What You'll Learn:
- Decompose composite shapes into simpler geometric shapes
- Calculate the area of each component shape
- Add individual areas to find the total area
- Apply this method to real-world composite figures
Khan Academy โ Area of Composite Shapes
Demonstrates splitting complex figures into simple shapes, calculating each area, then adding to get the total.
Watch on YouTubeFinding the Area of a Composite Figure โ Mr. J
Explains breaking down composite figures (rectangles, triangles) and adding areas with step-by-step examples.
Watch on YouTubeSurface Area Using Nets
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 cubes, prisms, and pyramids
Finding Surface Area Using Nets โ Math Mammoth
Unfolds 3D shapes into nets, computes each faceโs area, and adds to find total surface area (cubes, prisms).
Watch on YouTubeKhan Academy โ Surface Area Using Nets
Determines the surface area of prisms and pyramids using their nets with clear visuals and examples.
Watch on YouTubeVolume of Rectangular Prisms
Math Antics โ Volume
Introduces volume as the space inside a 3D object and applies V = l ร w ร h to rectangular prisms.
Watch on YouTubeKhan Academy โ Volume of a Rectangular Prism
Computes volume of rectangular prisms, including examples with fractional side lengths.
Watch on YouTubeComparing Surface Area and Volume
Khan Academy โ Volume and Surface Area Word Problems
Tackles word problems requiring both surface area and volume, emphasizing when to use each measurement.
Watch on YouTubeSurface Area and Volume Review โ Mario's Math Tutoring
Quickly reviews differences between surface area and volume and how to calculate both with examples.
Watch on YouTubeReal-World Application Problems
Khan Academy โ Volume and Surface Area Word Problems
Applies area, surface area, and volume to real scenarios, modeling and solving step-by-step.
Watch on YouTubeKhan Academy โ Volume Word Problem: Water Tank
Calculates the volume of a water tank from dimensions, applying the prism volume formula to a practical case.
Watch on YouTube