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Design & Measurement DM-L1 Objectives: Review Design & Measurement Formulas Learning Outcome B-3

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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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**Perimeter (Distance around the outside of a 2D shape) Units: cm, miles etc.**

Theory – Perimeter Formulas

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**Area (surface covered by a 2D shape) Units: cm2, ft2 etc.**

Theory – Area Formulas

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**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: cm3 or yd3 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. Theory – Volume of Prisms

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**Determine B, the area of the Base. Determine the Volume.**

Example for Practice

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**The second basic 3D object is a pyramid**

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. Find the Volume Theory – Volume of a Pyramid

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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. Find the Surface Area Theory – Surface Area of a Prism

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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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Find the Surface Area Example for Practice

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**For the bases of the cylinder and the cone:**

The formulas for the surface areas of objects with curved surfaces are as follows: For the bases of the cylinder and the cone: Theory – Cylinders, Cones, and Spheres

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**12" (inches or in) = 1' (foot or ft)**

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 cm 12" (inches or in) = 1' (foot or ft) 100 cm = 1m 36" = 1 yard or 1 yd 1000 m = 1 km 3' = 1 yd cm2 = 1 m2 144 in2 = 1 ft2 cm3 = 1 m3 9 ft2 = 1 yd2 27 ft3 = 1 yd3 Theory – Cylinders, Cones, and Spheres

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**All units for the garden are Feet**

Find the Perimeter Find the Area Example for Practice

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**All units for the granary are metres**

Find the Surface Area Find the Volume Example for Practice

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