Welcome to the guide on Shapes, Area, and Volume


Before you start: This is a longer lesson so feel free to skip over concepts you are already comfortable with


Basic concepts of shapes: (Properties of polygons) (Perimeter) (Classifying triangles) (Special right triangles) (Finding the apothem)

Note: Try to watch this video to get a better understanding of apothems, uses basic trigonometry


REMEMBER: Regular polygons are equiangular and equilateral, meaning all their sides are the same length and all their angles are the same degree.

Area: (Triangles) (Application: Finding the missing side of a rectangle given the area) (Parallelograms) (Pentagons) (Hexagons) (Advanced: Irregular shapes) (Area of a square using diagonals)

Note: Uses trigonometry


Volume and Surface Area: (Spheres-Formulas) (Volume and surface area for cuboids, rectangular prisms, and cubes)

Note: How can you modify the formula to only fit cubes? Remember, all the sides of a cube are the same length. (Triangular prisms) (Cylinders) (Cylinders-Video) (Cones) (Cones-Video) (Square and triangular pyramids)

Practice: (Area and perimeter of rectangles) (Area of polygons) (Composite shapes) (Surface area and volume) (Surface area of cubes and prisms) (Surface Area) (Volumes of cubes and prisms) (Surface area of prisms and pyramids) (Surface area of prisms and cylinders) (Surface area and volume of cones) (Surface area and volume of spheres) (Volume of pyramids and cones)



Check for Understanding (final review):









































































































*To look at the answers, click here*


Congrats on reaching the end of this lesson. If you did not understand any concept be sure to go back through and review, so that you can be fully prepared. We learn the most from our mistakes so don’t be disheartened by them. When you feel that you are ready, go ahead and take a little break. Then come back and move onto another section!