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Surface Area of Prisms & Cylinders. Identify the Solids. Named by the number of bases and the shape of the base. triangular prism. pentagonal prism. rectangular prism. hexagonal pyramid. square pyramid. “oblique” vs. “right”. oblique prism. oblique pyramid. right pyramid. right prism.
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Identify the Solids • Named by the number of bases and the shape of the base triangular prism pentagonal prism rectangular prism hexagonal pyramid square pyramid
“oblique” vs. “right” oblique prism oblique pyramid right pyramid right prism
P=45 4 9 Surface area (“Total Area”) vs Lateral Area • Lateral means sides only • find area of each rectangle • multiply by number of rectangles • 36 x 5 = 180 square units • or…..multiply perimeter by height • 45 x 4 = 180 square units A =36 45 4 9 9 9 9 9
The formula for finding the surface area of a prism is: SA = 2B + PH Where: B = Area of the Base P = Perimeter around the base H = the height of the prism
H +P SA = 2B Imagine we take the prism and “unroll” it. We are now looking at the net. Lets look at each part…
Surface Area of Prisms and Cylinders Looking at our formula, 4 S = 2B + PH 4 We start by finding the area of the base B = 4 X 4 = 16 We now need the perimeter of the base 8 P = 4 + 4 + 4 + 4 = 4 X 4 =16 H = 8 S = 2B + PH S = 2(16) + (16)8 S = 160 units2
Finding surface area in prisms is always the same, regardless of how complex the base’s area may be.
Then Multiply by 2 Looking at the NET again First we will find the area of the base
Area of the base = Surface Area of Prisms and Cylinders Plugging into our surface area formula 6 4 SA = 2B + PH 8 B = area of bases = 72 P = perimeter = 6 x 8 = 48 H = height = 8 Surface area = 2(72) + 48(8) = 528 units2
To find the surface area of a cylinder is very similar to the surface area of a prism. SA = 2B + PH SA = 2B + PH
SA = 2B + PH BASE: To find the surface area, we find the area of the base (which is a circle); so PERIMETER: Perimeter of the base (which is the circumference), HEIGHT: multiplied by the height of the cylinder
Height: 8 SA = 2B + PH Base Area: Circle Let’s try an example – Find Surface Area 4 8 Perimeter - the circumference: Plugging into the formula: 2B + PH
10” 12” sq. inches Find the surface area