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Lateral & Surface Area. of. Objectives. Concepts. Prisms. Discussions. Examples. Evaluation. Click a topic to start. Prepared by: Mr. Albert F. Perez. Quit. Objectives. Define a prism and identify it’s properties. Calculate the lateral area and surface area of right prisms.

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  1. Lateral & Surface Area of Objectives Concepts Prisms Discussions Examples Evaluation Click a topic to start Prepared by: Mr. Albert F. Perez Quit

  2. Objectives • Define a prism and identify it’s properties. • Calculate the lateral area and surface area of right prisms. • Apply formulas for lateral and surface area to real situations.

  3. A prism is a polyhedron with two identical polygonal faces,called bases,that lie in parallel planes.

  4. base vertex lateral face Altitude Lateral edge Click the part of the prism that you want to know. base

  5. I A H G D J B F E C The two parallel and congruent faces are called bases. Planes AIHGD and JFECB are bases

  6. I A H G D J B F E C Lateral edge is a segment joining the vertex of a prism and any vertex of its base. HF,GE,DC,AB, and I J are lateral edges.

  7. I A H G D J B F E C Lateral face is one of the parallelogram-shaped faces of the prism that connect the bases. Planes GDEC,ABCD, ABJI,FHIJ,and FHGE are lateral faces.

  8. A I H G D J B F E C Vertex is a point of intersection of the edges. Points A, B, C, D, E, F, G, H, I, J, are the vertices of a prism.

  9. Analtitude of a prism is a segment that is perpendicular to both bases with endpoints in the planes of the bases. The height (h) of the prism is the length of the altitude height

  10. Types of Prism Right prism Oblique prism

  11. These are oblique prisms. Oblique rectangular prism Oblique Pentagonal prism

  12. These are right prisms. Triangular prism Pentagonal prism cube Rectangular prism

  13. D C E A F A B B E F C D “This is a net showing the lateral area of a prism.”

  14. “The sum of areas A, E C, and F is the lateral area of the prism.” A B E F C D

  15. A B E F 8cm 5cm C 4cm 4cm 8cm 5cm D “Lateral Area = A + C + F + E. =(8cm)(5cm)+(8cm)(5cm)+(4cm)(5cm)+(4cm)(5cm) = 5cm ( 8cm + 8cm + 4cm + 4cm) = 5cm [2(8cm) + 2(4cm)] Think: 5cm is the height of the prism 2(8cm) + 2(4cm) is the perimeter of the base.”

  16. The lateral area (LA) of a right prism is the product of the perimeter of its base and the height of the prism. 3cm LA = [2(5cm) + 2(2cm)] [3cm] LA =42cm2 2cm 5cm LA = ph

  17. D C E A F A B E F B C D “This is a net showing the surface area of a prism.”

  18. A E F B 8cm 5cm 4cm 4cm 8cm C 5cm D 4cm 8cm “Surface Area = A + C + F + E + B + D = ph + (8cm)(4cm) + (8cm)(4cm) = ph + 2[(8cm)(4cm)] Think: (8cm)(4cm) is the area of the base of the prism.

  19. The surface area (SA) of a prism is the sum of the lateral area and the areas of the two bases. SA= 42cm2 + 2(10cm2) SA=62cm2 3cm 2cm 5cm SA = LA + 2B

  20. 6cm 8cm 9cm 10cm Find the lateral area of the right triangular prism. LA = ph Solution: LA =(6+8+10)(9)=216cm2 Find the surface area of the prism. SA = LA + 2B Solution: SA = 216+2(1/2)(8)(6) = 216+48=264 cm 2

  21. C Solution: LA = ph = (14+14+14)(20) = (42)(20) = 840 sq.units SA = ph + 2B = 840 + 2(1/2•14•7√3 ) = 840 + 98√3 sq.units D B x A B Find the lateral area and the surface area of the right equilateral triangular-based prism shown, if AB =14 and AD=20.

  22. Find the altitude of a right prism for which the area of the lateral surface is 143 sq. units and the perimeter of the base is 13units. Given: LA = 143 sq.units , perimeter = 13 Altitude = ? Solution: LA = ph 143 = (13) h 11 = h

  23. A B D C E F G H 1. Plane ABCD is a _______. a. Lateral face b. face c.base 2.Whichis NOT a lateral edge? a.BE b.AD c.DG Choose the letter of the best answer. Use the figure above.

  24. 3. The lateral faces of a right prism are _____ rectangles. a.always b.sometimes c.never 4. The altitude of a right prism is ______ the height of the prism. a.always b.sometimes c.never 5. The two bases of a prism _____ differ in their total number of edges. c.never b.sometimes a.always Choose the letter of the best answer.

  25. 1.The lateral faces of a cube are squares. Find the surface area of a cube whose base edge length is 5 cm. 2.The perimeter of a base of a right prism is 37 cm and a lateral edge is 22 cm. Find the lateral area of the prism. a. 150 cm2 b. 250 cm2 c. 200 cm2 a. 840 cm2 b. 850 cm2 c. 814 cm2 Click the letter of the correct answer.

  26. 3.The surface area of a cube is 294 cm2.What is the length of its side? a. 49 cm b. 7 cm c. 17 cm 4. Find the lateral area of a right triangular prism with a height of 20 in and a right triangular base with legs of 8 in and 6 in. a. 528 in2 c. 480 in2 b. 490 in2 Click the letter of the correct answer.

  27. 5. Many baking pans are given special coating to make food stick to the surface less. A rectangular cake pan is 9in by 13in and 2in deep.What is the area of the surface to be coated? a. 234 in2 b. 250 in2 c. 205 in2 Click the letter of the correct answer.

  28. 6.How many square meters of fabric do you need to cover a suitcase with dimensions 0.9m by 0.7m by 0.2 m? a. 19 m2 b. 1.9 m2 c. 0.19 m2 Click the letter of the correct answer.

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