Chapter 11: Measuring Length and Area Section 11.1: Areas of Triangles and Parallelograms

English Length 1 foot = 12 inches 1 yard = 3 feet = 36 inches 1 mile = 1,760 yd = 5280 feet = 63,360 in

The Metric System distance volume weight Based on a base 10 number system The prefixes are: kilo (k), hecto (h), deka (da), deci (d), centi (c), and milli (m) Used as the standard measurement system in Europe Meters are used to measure Liters are used to measure Grams are used to measure distance volume weight

Conversions: To convert from a larger metric unit of measure to a smaller one, multiply by a multiple of 10 To convert from a smaller metric unit of measure to a larger one, divide by a multiple of 10 SHORTCUT: Use “King Henry Died By Drinking Chocolate Milk”

King Henry Died By Drinking Choc. Milk T O E K A A S E U N I T E N T I I L I L O E C I Ex: Convert the following measurements: 1) 9.82 m = ? mm 2) 10.543 mg = ? kg 0.000010543 9820

Section 11.1: Areas of Triangles and Parallelograms Area: the amount of surface covered by a figure Measured in square units (in2, ft2, yd2, m2, etc…) Area of a rectangle: A = bh Since a square has the same length for all sides: A = s2 h b s

Section 11.1: Areas of Triangles and Parallelograms Find the area of the square Find the area of the rectangle 20 in 4 m 20 m

Section 11.1: Areas of Triangles and Parallelograms The rectangle has an area of 98 cm2. Find the length of its base A square has an area of 64 ft2. Find the length of its sides 7 cm

Section 11.1: Areas of Triangles and Parallelograms Dividing a Complex Polygon into Rectangles: Find the dimensions of rectangles A and B: A 2 6 3 3 B 12

Section 11.1: Areas of Triangles and Parallelograms Find the area of the polygon made up of rectangles 4 in 3 in 10 in 7 in 15 in 14 in

Section 11.1: Areas of Triangles and Parallelograms Area (triangle) = ½ bh Remember the base and the height must be perpendicular to each other h h h b b b

Section 11.1: Areas of Triangles and Parallelograms Find the area of the following triangles: Find the height of a triangle if the area is 124 ft2 and the base is 30 ft. 7 in 10.5 in 65 cm 8 in 25 cm 3 in 5 in 60 cm

Section 11.2: Areas of Trapezoids and Kites Area (trapezoid) = ½ h(b1 + b2) Remember: the bases are parallel to each other! b1 h b2

Section 11.2: Areas of Trapezoids and Kites Area (kite/rhombus) = ½ d1  d2

Section 8.4: Area of Triangles Areas of Similar Polygons: If two polygons are similar with a scale factor of , then the ratio of their areas is b a

Section 8.4: Area of Triangles The following triangles are similar. Find the scale factor of ΔABC to ΔDEF. Find the scale factor of the areas of ΔABC to ΔDEF. 6 18 4.87 14.62 7 21