In this Grade 8 Saxon Math Course 3 lesson, students learn to calculate total surface area and lateral surface area of prisms and other three-dimensional solids, including cubes, rectangular prisms, and buildings. Students apply the formula for lateral surface area by multiplying the perimeter of the base by the height, and use nets as two-dimensional models to visualize and find the combined area of a solid's faces. The lesson builds spatial reasoning skills through real-world examples such as estimating the surface area of a cereal box.
Section 1
📘 Surface Area
The surface area of a solid is the combined area of the surfaces of the solid. We can find the lateral surface area of a prism by multiplying the perimeter of the base by the height.
This card introduces the core idea of surface area. Next, you'll work through examples calculating both total and lateral surface area for different solids.
Section 2
Surface Area
The surface area of a solid is the combined area of the surfaces of the solid. We distinguish between total surface area and lateral surface area, which is the combined area of surfaces on the sides of a solid and does not include the area(s) of the base(s).
A cube with 5 cm edges has 6 faces. The total surface area is .
The lateral surface area of the same cube only includes the 4 side faces: .
A box measuring 4 in long, 3 in wide, and 5 in high has a lateral area of .
Think of a gift box. If you unfolded it completely flat, the total surface area would be the area of all the cardboard. Lateral surface area is just the sides, ignoring the top and bottom. It is like measuring the paper needed to wrap the box’s body, but not the lid or the base.
Section 3
Finding Lateral Surface Area
We can find the lateral surface area of prisms and cylinders by multiplying the perimeter or circumference of the base by the height.
A cube with 8 cm edges has a base perimeter of . Lateral area is .
A building with a base perimeter of 120 ft and height of 15 ft has a lateral area of .
A tissue box is 9 in by 5 in at the base. Its perimeter is . With a height of 4 in, the lateral area is .
Imagine peeling the label off a soup can. When you lay it flat, it becomes a rectangle! The rectangle's height is the can’s height, and its length is the circle's circumference. This same cool trick works for the sides of a prism; it is just the base's perimeter multiplied by the object's height.
Section 4
A Net of a Solid
A net is a two-dimensional image of the surfaces of a solid. A net can help us visualize a solid's surfaces.
A net for a cube consists of six identical squares connected by their edges, often arranged in a cross shape.
To find a cereal box's surface area, sketch its net: a front, back, top, bottom, and two side rectangles.
The net of a triangular prism is made of two triangles for the bases and three rectangles for the sides.
Think of a net as a solid's blueprint or a flat-packed cardboard box before you assemble it. It shows you every single face of the object all at once, laid out flat on a table. This makes it super easy to see all the individual shapes you need to add up to find the total surface area.
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Section 1
📘 Surface Area
The surface area of a solid is the combined area of the surfaces of the solid. We can find the lateral surface area of a prism by multiplying the perimeter of the base by the height.
This card introduces the core idea of surface area. Next, you'll work through examples calculating both total and lateral surface area for different solids.
Section 2
Surface Area
The surface area of a solid is the combined area of the surfaces of the solid. We distinguish between total surface area and lateral surface area, which is the combined area of surfaces on the sides of a solid and does not include the area(s) of the base(s).
A cube with 5 cm edges has 6 faces. The total surface area is .
The lateral surface area of the same cube only includes the 4 side faces: .
A box measuring 4 in long, 3 in wide, and 5 in high has a lateral area of .
Think of a gift box. If you unfolded it completely flat, the total surface area would be the area of all the cardboard. Lateral surface area is just the sides, ignoring the top and bottom. It is like measuring the paper needed to wrap the box’s body, but not the lid or the base.
Section 3
Finding Lateral Surface Area
We can find the lateral surface area of prisms and cylinders by multiplying the perimeter or circumference of the base by the height.
A cube with 8 cm edges has a base perimeter of . Lateral area is .
A building with a base perimeter of 120 ft and height of 15 ft has a lateral area of .
A tissue box is 9 in by 5 in at the base. Its perimeter is . With a height of 4 in, the lateral area is .
Imagine peeling the label off a soup can. When you lay it flat, it becomes a rectangle! The rectangle's height is the can’s height, and its length is the circle's circumference. This same cool trick works for the sides of a prism; it is just the base's perimeter multiplied by the object's height.
Section 4
A Net of a Solid
A net is a two-dimensional image of the surfaces of a solid. A net can help us visualize a solid's surfaces.
A net for a cube consists of six identical squares connected by their edges, often arranged in a cross shape.
To find a cereal box's surface area, sketch its net: a front, back, top, bottom, and two side rectangles.
The net of a triangular prism is made of two triangles for the bases and three rectangles for the sides.
Think of a net as a solid's blueprint or a flat-packed cardboard box before you assemble it. It shows you every single face of the object all at once, laid out flat on a table. This makes it super easy to see all the individual shapes you need to add up to find the total surface area.
Book overview
Jump across lessons in the current chapter without opening the full course modal.
Continue this chapter