Polygons, Cones, Right Circular Cylinders, and Right Rectangular Prisms UMI: July 13, 2016

Simple: does not intersect itself Closed: Curve can be drawn starting and stopping at the same point. Segment: Straight line Polygons. Polygons are simple closed curves with sides that are only segments.

Polygons and Non-polygons.

Practice 1: What is the perimeter of the rectangle? Perimeter of Polygons The perimeter of Polygons is the sum of lengths of its sides.

Practice 2: What is the perimeter of This polygon? Solution :

Practice 3: Graph the polygon ABCDEF, which has vertices A(-3,3) B(1,3) C(1, 1) D(4, 1) E(4, -3) F(-3, -3); What is the perimeter of the polygon, ABCDEF? Solution :

Area of Polygons The area of a polygon is the number of square units inside that polygon. Example: Find the area of the following polygons

The Area of a Rectangle Put the shape on a grid and count the number of squares The rectangle has an area of 15. If each square was 1 cm on a side, then the area would be 15 cm 2 (15 square cm) The formula is: Area = w × h w = width, h = height The width is 5, and the height is 3, so we know w = 5 and h = 3: Area = 5 × 3 = 15

The Area of a Triangle

The Area of Popular Polygons

Example: Sam cuts grass at $0.10 per square meter. How much does Sam earn cutting this area: Solution : Part A is a square: Area of A = a 2 = 20m × 20m = 400m 2 Let's break the area into two parts: Part B is a triangle. Viewed sideways it has a base of 20m and a height of 14m. Area of B = ½b × h = ½ × 20m × 14m = 140m 2 Area = Area of A + Area of B = 400m m 2 = 540m 2 Sam earns = $0.10 × 540m 2 = $54

Practice 1: What is the area of the trapezoid? Solution :

Practice 2: What is the area of the octagon? Solution :

Right Circular Cylinders A circular cylinder is a closed solid that has two parallel circular bases connected by a curved surface. Right Circular Cylinders: When the two circular bases are exactly over each other and the axis is a right angles to the base, this is a called a 'right circular cylinder'.

Surface Area of the Right Circular Cylinders

Derivation The surface area of a cylinder can be found by breaking it down into three parts: 1.The two circles that make up the ends of the cylinder. 2.The side of the cylinder, which when "unrolled" is a rectangle

Derivation

Volume of the Right Circular Cylinders

Practice 1: The diagram shows a cylinder of diameter 20 units and height 9 units. Find the surface area of the cylinder. Solution :

Practice 2: The diagram shows a cylinder of height 4 units and diameter 4 units. What is its volume? Solution :

Right Rectangular Prisms A prism is a solid that has two faces that are parallelparallel and congruent. These are called the bases of the prism.congruent Right Rectangular Prisms 1.The bases are rectangles 2.The bases are exactly one above the other. This means that lines joining corresponding points on each base are perpendicular to the bases

Surface Area of the Right Rectangular Prism Which can be shortened to

Volume of the Right Rectangular Prism

Practice 1: Find the surface area and the volume of this right rectangular prism Solution :

Practice 2: Find the surface area and the volume of this right rectangular prism Solution :

Thank You References: 1.A problem solving approach to mathematics for elementary school teachers by Billstein, Libeskind, Lott 2.Math is Fun : 3.Math Open Reference: