Worksheet 8.2B - Total Surface Areas of Prisms - Base and Surface Area

Sep 18, 2026

Uploaded by Connor

Worksheet 8.2B focuses on understanding prism bases and calculating total surface area. It explains that the prism base is the bottom layer and that the prism is completed by stacking the same base shape, illustrated with a triangular prism example. Key formulas connect lateral faces and base perimeter/area. Practice questions cover triangular, cuboid-derived, and pentagonal prisms, including solving for unknown dimensions using given total surface areas or volumes, plus a real-world painting cost application.

LanguageEnglish

CategoryExam

FormatPDF

Pages7

Reading Time18 min

AccessFree to download

How to find the base of prism?

Key points

Lateral faces area relation

Total surface area formula

Example: triangular prism base type

Practice questions

Problems 1-6

Problems 7-12

Problems 13-14

Problem 15 (pen holder & painting cost)

Answers

Worksheet 8.2B Total Surface Areas of Prisms Name: ( ) Class: Date: How to find the base of prism? The "base" of the prism can be understood as the "foundation" of the prism, which is equal to the bottom layer of the cupcake. To complete the cupcake, we can add decoration to the layer freely. However, to complete the prism, we cannot freely add decoration. On top of the base , We need to stack (疊) the same figure of the base. Take the triangular prism (三棱柱/三角柱體) as an example Example: Is the base of the upper prism "a triangle" or "a rectangle ''? Think, if the base of the upper prism is a rectangle , can we stack the rectangles and create the prism? Actually, the upper prism is a horizontally placed triangular prism(三棱柱/三角柱體), and the bottom of the triangular prism is a triangle. Key Points 1. Total area of all lateral faces ofa prism = perimeter of base 􀁵 height 2. Total surface area of a prism = total area of all lateral faces + 2 􀁵 base area Self learning video: [https://qrgo.page.link/zRgUH](https://qrgo.page.link/zRgUH) 1. The figure shows a triangular prism. (a) Find the total area of all its lateral faces. (b) Find its total surface area. Solution (a) (b) Find the total surface areas of the following prisms. (2 – 3) 7 cm 24 cm 4. In the figure, the total surface area of the cuboid is 318 cm2. (a) Find the area of ABCD. (b) Hence, find the value of x. Solution (a) (b) 5. In the figure, the total surface area of the prism is 276 cm2. (a) Find the area of PQRS. (b) Hence, find the value of x. Solution (a) (b) A 6 cm B 9 cm C P Q R S x cm 4 cm 5 cm 12 cm 6. The figure shows a pentagonal prism. Its base is a regular pentagon with side length 4 cm. (a) Find the total surface area of the prism. (b) It is given that the cost of painting each 5 cm2 of the surface of the prism is $2.2 . How much does it cost to paint the surface of the prism? Solution (a) (b) 7. The figure shows a prism with volume 1200 cm3. (a) Find the value of x. (b) Find the total surface area of the prism. 15 cm Solution (a) (b) 13 cm 10 cm 8 cm x cm 6 cm 4 cm area = 27.5 cm2 Find the total surface areas of the following prisms. (8 – 12) 8. 8 cm 8 cm 5 cm 15 cm 3 cm 9. 20 cm 12 cm 10 cm 6 cm 6 cm 10. 15 cm 13 cm 13 cm 20 cm 15 cm 6 cm 12 cm 12 cm Solution Solution Solution 11. Solution 12 cm 20 cm 16 cm 12 cm 15 cm 12. Solution 10 cm ~~ ~~ 10 cm 8 cm 14 cm 6 cm cm 12 cm Find the value of x in each of the following prisms. (13 – 14) 13. 4 cm 8 cm 4 cm 8 cm x cm 12 cm total surface area = 328 cm2 Solution 14. 12 cm total surface area = 664 cm2 Solution 15. Kenny makes a cardboard pen holder in the shape of prism as shown in the figure. (a) Find the total outer surface area of this pen holder. (b) Kenny wants to make 5 such pen holders and paint the outer surface of the pen holders. The painting cost for each 4 cm2 on the outer surface is $0.05 . How much does it cost to paint all the 5 pen holders? Solution (a) (b) 答案： 1. (a) 560 cm2 (b) 728 cm2 2. 330 cm2 3. 688 cm2 4. (a) 54 cm2 (b) 7 5. (a) 48 cm2 (b) 6 6. (a) 175 cm2 (b) $77 7. (a) 12 (b) 700 cm2 8. 400 cm2 9. 1152 cm2 10. 1320 cm2 11. 1592 cm2 12. 856 cm2 13. 5 14. 7 15. (a) 440 cm2 12 cm 8 cm (b) $27.5

FAQs

How is the base of a prism defined in this worksheet?

The base is the prism’s “foundation,” equal to the bottom layer shape. The prism is formed by stacking the same base figure on top.

What is the relationship for the lateral faces area of a prism?

The total area of all lateral faces of a prism equals the perimeter of the base multiplied by the height.

How do you calculate the total surface area of a prism?

Total surface area equals the total area of all lateral faces plus two times the base area.

Sep 18, 2026

Uploaded by Connor