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

2. 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

3. Perimeter (Distance around the outside of a 2D shape) Units: cm, miles etc.
Theory – Perimeter Formulas

4. Area (surface covered by a 2D shape) Units: cm2, ft2 etc.
Theory – Area Formulas

5. 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

6. Determine B, the area of the Base. Determine the Volume.
Example for Practice

7. 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

8. 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

9. 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

10. Find the Surface Area
Example for Practice

11. 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

12. 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

13. All units for the garden are Feet
Find the Perimeter
Find the Area
Example for Practice

14. All units for the granary are metres
Find the Surface Area
Find the Volume
Example for Practice