File: GeomB 2011 Answers 8.10.11 No Calculators: Updated: August 10‚ 2011 A concave polygon looks sort of like a vertex has been ’pushed in’ towards the inside of the polygon. A convex polygon has all the vertices of the polygon pointing outwards‚ away from the interior of the shape. Think of it as a ’bulging’ polygon. A regular polygon is a polygon which is equiangular (all angles are congruent) and equilateral (all sides have the same length). Regular polygons may be convex or star. (5
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Surface Area Formulas In general‚ the surface area is the sum of all the areas of all the shapes that cover the surface of the object. Cube | Rectangular Prism | Prism | Sphere | Cylinder | Units Note: "ab" means "a" multiplied by "b". "a2" means "a squared"‚ which is the same as "a" times "a". Be careful!! Units count. Use the same units for all measurements. Examples |Surface Area of a Cube = 6 a 2
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BE PROPERLY STAPLED. 1. Are the two rectangular prisms similar? If so‚ give the similarity ratio. 2. The lateral areas of two similar paint cans are 1019 cm2 and 425 cm2. The volume of the small can is 1157 cm3. Find the volume of the large can. 3. The volumes of two similar solids are 128 m3 and 250 m3.The surface area of the larger solid is 250 m2. What is the surface area of the smaller solid? 4. Triangular Prism X and triangular Prism Y are similar. The ratio of corresponding dimensions
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Intro: Surface Area and Volume Multiple Choice Identify the choice that best completes the statement or answers the question. Find the surface area of the space figure represented by the net. ____ 1. 12 in. 4 in. 6 in. 4 in. 4 in. 6 in. a. 288 in.2 ____ 2. b. 144 in.2 c. 240 in.2 d. 288 in.2 5 cm 5 cm 7 cm 8 cm 4 cm ____ a. 124 cm2 b. 110 cm2 c. 150 cm2 d. 164 cm2 3. Find the surface area of the cylinder. Use a calculator. Round to the nearest tenth. 4m 3m a
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Surface area Surface area is the measure of how much exposed area a solid object has‚ expressed in square units. Mathematical description of the surface area is considerably more involved than the definition of arc length of a curve. For polyhedra (objects with flat polygonal faces) the surface area is the sum of the areas of its faces. Smooth surfaces‚ such as a sphere‚ are assigned surface area using their representation as parametric surfaces. This definition of the surface area is based on methods
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Surface area and Lateral surface area of Polyhedrons LSA or Lateral Surface Area refers to the sum of the areas of all the faces of a three-dimensional figure‚ excluding its bases. SA or Surface Area- refers to the sum of the areas of all the faces of a three-dimensional figure. It also referred to as the Total Surface Area (TSA). ~~~~~~~~~~~~~~~~~~~ For Rectangular Prism LSA= P(h) *where P=perimeter of the base ; h= measurement of the height SA= 2B+ LSA *where B= area of the
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Area of some rectilinear figures Area of a Triangle : 1/2 x Base x Heights Area of Equilateral Triangle : Sqrt(3)/4 x (Side)2 Area of a Triangle - Hero’s formula : Sqrt{s (s - a) (s - b) (s - c)} where 2s = a + b + c. Area of Rectangle = Length x Breadth Area of a Square = (Side)2 Area of Four Walls = 2 x height (Length + breadth) Area of Rhombus = 1/2 x (Products of Diagonals) Area of Trapezium = 1/2 x (Sum of Parallel Sides) x (Distance between Parallel lines) Area of Parallelogram
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Performance Task in GEOMETRY * Computation of the surface area‚ amount and type of needed material and the volume of the package. Volume V= L x H x W = (23 cm) (4 cm) (12cm) = (276) (4) = 1 104 cm Area A= L x W = (23cm) (12cm) = 276cm Surface Area A= 2(Lh) + 2(Lw) + 2(Wh) / 2( lh + lw + wh) = 2(23*4) + 2(23*12) + 2(12*4) = 2(92) + 2(276) + 2(48)
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Report Hypothesis: I predict that as the surface area of the canopy increases‚ the time it takes for the parachute to fall also increases. This is because the air resistance is larger‚ therefore the drag is increased. So the speed of the parachute decreases. This is because the forces (air resistance and gravity) are unbalanced. The change in air resistance is important because the larger the surface area of the canopy‚ the more air particles it is ‘hitting’; therefore the air
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apply before an area can be considered safe? A safe area according to the definition from the Encarta is summed up as an area where one can find refuge and safety‚ while living in security‚ (Encarta. 2007). Would you consider the Ryerson Campus area to be safe? This depends on a certain individual ’s bias which is based on the gender and age of that individual. Another factor that comes in to play is the time of day you are viewing the area‚ different opinions may be generated on an area if it were daytime
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