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40S Applied Math Mr. Knight – Killarney School Slide 1 Unit: Design & Measurement Lesson: DM-L1 Design & Measurement Learning Outcome B-3 DM-L1 Objectives: Review Design & Measurement Formulas

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40S Applied Math Mr. Knight – Killarney School Slide 2 Unit: Design & Measurement Lesson: DM-L1 The purpose of this lesson is to review the formulas for perimeter and area of squares, rectangles, parallelograms, trapezoids, triangles, and circles, as well as the surface area and volume of prisms, pyramids, cylinders, cones, and spheres. These formulas will be used to solve problems. Theory – Intro

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40S Applied Math Mr. Knight – Killarney School Slide 3 Unit: Design & Measurement Lesson: DM-L1 Perimeter (Distance around the outside of a 2D shape) Units: cm, miles etc. Theory – Perimeter Formulas

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40S Applied Math Mr. Knight – Killarney School Slide 4 Unit: Design & Measurement Lesson: DM-L1 Area (surface covered by a 2D shape) Units: cm 2, ft 2 etc. Theory – Area Formulas

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40S Applied Math Mr. Knight – Killarney School Slide 5 Unit: Design & Measurement Lesson: DM-L1 Volume (space occupied by 3D figures). A prism is a 3D solid where the shape of the base is maintained throughout the height. A prism may also be defined as a 3D solid where two faces, called bases, are congruent and parallel polygons, and the other (lateral) sides are rectangles. The volume of a prism can be determined by multiplying the area of the base by the height of the prism. The diagram below shows a rectangular and a trapezoidal prism. Units: cm 3 or yd 3 Theory – Volume of Prisms The volume of a prism is: V = BH, where B is the area of the base, and H is the height of the 3D object.

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40S Applied Math Mr. Knight – Killarney School Slide 6 Unit: Design & Measurement Lesson: DM-L1 Determine B, the area of the Base. Determine the Volume. Example for Practice

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40S Applied Math Mr. Knight – Killarney School Slide 7 Unit: Design & Measurement Lesson: DM-L1 The second basic 3D object is a pyramid. This is a 3D object with a polygon as a base and triangular sides that meet at one point. The volume of the pyramid is where B is the area of the base and H is the height of the pyramid. Theory – Volume of a Pyramid Find the Volume

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40S Applied Math Mr. Knight – Killarney School Slide 8 Unit: Design & Measurement Lesson: DM-L1 The surface area (S.A.) of a prism is the sum of the surface areas of the two bases and the sides (known as the lateral surfaces). The formula for the surface area of a prism is: S.A. = 2B + PH where S.A. refers to the total Surface Area, B the area of the base, P the perimeter of the base, and H the height of the object. Theory – Surface Area of a Prism Find the Surface Area

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40S Applied Math Mr. Knight – Killarney School Slide 9 Unit: Design & Measurement Lesson: DM-L1 The surface area (S.A.) of a pyramid is the sum of the area of the base and the areas of the triangular sides. Please note that, in this course, the bases are regular polygons and the sides are isosceles triangles. The formula for the surface area of a pyramid is: where S.A. refers to surface area, B the area of the base, P the perimeter of the base, and l the 'slant height' or the altitude of the isosceles triangles. Theory – Surface Area of a Prism

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40S Applied Math Mr. Knight – Killarney School Slide 10 Unit: Design & Measurement Lesson: DM-L1 Example for Practice Find the Surface Area

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40S Applied Math Mr. Knight – Killarney School Slide 11 Unit: Design & Measurement Lesson: DM-L1 Theory – Cylinders, Cones, and Spheres The formulas for the surface areas of objects with curved surfaces are as follows: For the bases of the cylinder and the cone:

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40S Applied Math Mr. Knight – Killarney School Slide 12 Unit: Design & Measurement Lesson: DM-L1 Theory – Cylinders, Cones, and Spheres All units must be either metric system (S.I.) or Imperial system units when calculating perimeter, area, surface area, or volume. The table shows units that will be used in this course. Metric System (S.I.)Imperial System 10 mm = 1 cm12" (inches or in) = 1' (foot or ft) 100 cm = 1m36" = 1 yard or 1 yd 1000 m = 1 km3' = 1 yd 10 000 cm 2 = 1 m 2 144 in 2 = 1 ft 2 1 000 000 cm 3 = 1 m 3 9 ft 2 = 1 yd 2 27 ft 3 = 1 yd 3

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40S Applied Math Mr. Knight – Killarney School Slide 13 Unit: Design & Measurement Lesson: DM-L1 Example for Practice All units for the garden are Feet Find the Perimeter Find the Area

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40S Applied Math Mr. Knight – Killarney School Slide 14 Unit: Design & Measurement Lesson: DM-L1 Example for Practice All units for the granary are metres Find the Surface Area Find the Volume

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