Area: Day 1 Math 10-3 Ch.3 Measurement

Area- basics Area is the surface of a 2-D object. A good way to visualize area is to imagine coloring in between the lines of a shape; when you have done this, you have colored the area. When we calculate the area, we are finding the “square” units of the shape.

Area - basics For example, the area of a 2ft by 4 ft concrete slab would be 8 ft 2 “Squaring” means multiplying something by itself. In the example, we multiplied ft x ft together to get ft 2 OR “square foot”.

When will I use this? Contractors and other tradespersons often use grid paper to help them envision the work site. Grid paper usually has 1 cm by 1 cm squares, which a contractor may use to represent 1 ft by 1ft.

Grid Paper – 1 cm x 1 cm

Estimating…. We can also use referents to determine the area of certain spaces or objects. Remember a referent is a known measure used for estimating or comparing. For example, the tip of your thumb is about 1 cm x 1 cm = 1 cm 2 (1 square centimeter) Or the area of the palm of your hand is about 4 in x 4 in = 16 in 2 (16 square inch) The area of a typical floor tile is approximately 1 ft x 1ft = 1 ft 2 (1 square foot)

Basic Area Formulas There are formulas we can use to calculate the area of basic shapes: Area Square = side x side = s x s OR s 2 Area Rectangle = length x width = l x w

The formulas for more complex shapes are a bit trickier. First we need to review a few basics… A polygon is a closed figure with straight sides. We discussed a few polygons yesterday such as triangles, trapezoids and parallelograms. The height of an object is the perpendicular distance from the base of a polygon to an opposite vertex. Perpendicular – two lines that form a right (90 0 ) angle. For example, a corner is a 90 0 angle. Vertex – the point where two or more lines meet.

Triangle Area triangle = (base x height) OR b x h remember, multiplying by is the same as dividing by 2!

Parallelogram Area Parallelogram = base x height OR b x h

Trapezoid Area Trapezoid = (base + opposite side) x height OR (b1+b2) x h

Circle Area Circle = x radius x radius OR r 2

Ex1. Arthur is planning his living room space. He knows that the coffee table is 2.5 m long by 1.5 m wide. What is the area of the table? Sketch it! Formula! Area Rectangle = l x w = 2.5m x 1.5 m = 3.75 m 2 * It is very important to include your UNITS for area. The units will always be the measurement unit 2 !

Ex2. Arthur wants to put a circular decorative stand in the room as well. The radius of the stand is 2 m. What is the area of the stand? Sketch it! Formula! Area circle = r 2 = 3.14 x 2 x 2 = m 2