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**Surface Area: Prisms and Pyramids**

Unit Five Lesson 6 Surface Area: Prisms and Pyramids

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**3 easy steps to calculate the Surface Area of a solid figure**

Determine the number of surfaces and the shape of the surfaces of the solid Apply the relevant formula for the area of each surface Sum the areas of each surface

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**Surface Area – Basic concept**

4 rectangular faces and 2 square faces Surface Area – Basic concept rectangle rectangle rectangle square square rectangle Determine the number and shape of the surfaces that make up the solid. When you’ve done all that find the area of each face and then find the total of the areas. It might be easier to think of the net of the solid.

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**Four rectangular faces**

Square prism Find the surface area of this figure with square base 5 cm and height 18 cm Two square faces Four rectangular faces 18 cm 5 cm

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**Rectangular prism Now sum these areas 20 cm 15 cm 5 cm**

Find the surface area of this figure with length 10 cm, width 15 cm and height 12 cm. Now sum these areas 20 cm 15 cm 5 cm

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Surface Area of Prisms The surface area of a prism is the entire area of the outside of the object. To calculate surface area, find the area of each side and add them together. There are 6 faces to this rectangular prism. Front and back are the same Top and Bottom are the same Two ends are the same.

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Surface Area of Prisms To find the surface area, add the areas together. Top and Bottom A = bh A = (90)(130) A = cm2 Ends A = bh A = (90)(50) A = 4500 cm2 Front and back A = bh A = (130)(50) A = 6500 cm2 Total Surface Area = 2(top and Bottom) + 2(Ends) + 2(Front and Back) = 2(11700) + 2(4500) + 2(6500) = cm2

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YOU TRY! To find the surface area, add the areas together.

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**SOLUTION To find the surface area, add the areas together.**

Top and Bottom A = bh A = (4)(10) A = 40 m2 Ends A = bh A = (2)(4) A = 8 m2 Front and back A = bh A = (2)(10) A = 20 m2 Total Surface Area = 2(top and Bottom) + 2(Ends) + 2(Front and Back) = 2(40) + 2(8) + 2(20) = 136 m2

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**Triangular Prism 1 2 3 height 8 cm Recall**

Find the surface area of this figure with dimensions as marked. 12 cm 10 cm 6 8 height 8 cm 12 cm 20 cm 10 cm Hence, total surface area Determine the number of faces and the shape of each face Recall 1 Apply the area formulae for each face 2 Sum the areas to give the total surface area 3

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**Square Pyramid P height 13 cm. 13 12 10 T**

Hence, total surface area Square Pyramid Find the surface area of this figure with square base 10 cm and height 12 cm. 10 13 T P height 13 cm. 4 triangular faces with the same dimensions and 1 square face We need to find the height of each triangular face. 12

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**Surface Area of Triangular Prisms**

The surface area of a triangular prism is the entire area of the outside of the object. To calculate surface area, find the area of each side and add them together. There are 5 faces to this triangular prism. Two ends are the same. Three sides depend on the type of triangle: Equilateral Isosceles Scalene

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**Surface Area of Triangular Prisms**

To find the surface area, add the areas together. Bottom A = bh A = (1.3)(2.1) A = 2.73 m2 Ends A = bh 2 A = (1.3)(0.5) 2 A = m2 Front A = bh A = (2.1)(0.5) A = 1.05 m2 Back A = bh A = (2.1)(1.2) A = 2.52 m2 Total Surface Area = Bottom + 2(Ends) + Front + Back = (0.325) = 6.95 m2

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YOU TRY! To find the surface area, add the areas together.

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**SOLUTION To find the surface area, add the areas together. Sides**

Height = .866 a2 = c2 - b2 a2 = (1)2 - (0.5)2 a2 = a2 = 0.75 a = 0.866 Sides A = bh A = (1)(3) A = 3 m2 Ends A = bh 2 A = (1)(0.866) 2 A = m2 Total Surface Area = 2(Ends) + 3(sides) = 2(0.433) + 3(3) = m2

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**Surface Area of Pyramids**

The surface area of a pyramid is the entire area of the outside of the object. To calculate surface area, find the area of each side and add them together. There are 5 faces to this triangular pyramid. One square bottom Four triangular sides are the same.

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**Surface Area of Pyramids**

To find the surface area, add the areas together. Bottom A = s2 A = (4)(4) A = 16 cm2 sides A = bh 2 A = (4)(3) 2 A = 6 cm2 Total Surface Area = Bottom + 4(sides) = (6) = 40 cm2

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YOU TRY! To find the surface area, add the areas together.

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**SOLUTION To find the surface area, add the areas together. Bottom**

A = 25 cm2 sides A = bh 2 A = (5)(6) 2 A = 15 cm2 Total Surface Area = Bottom + 4(sides) = (15) = 85 cm2

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Practice page 178 and 179 Odd #1 - 13

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