A = ½ x b x h or ½bh or bh. Formula Key A 2 + B 2 = C 2. Pythagorean Theorem. Perimeter. b or (b 1 / b 2 for a trapezoid) height
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1 Formula Key b 1 base height rea b or (b 1 / b for a trapezoid) h b Perimeter diagonal P d (d 1 / d for a kite) d 1 d Perpendicular two lines form a angle. Perimeter P = total of all sides (side + side + side + side ) Perimeter Pythagorean Theorem To find the perimeter of any shape add all the side lengths together. + = =3 inches The perimeter is 3 in. 8 inches 6 inches 8 inches = = 100 = 100 = = inches rea of a triangle rea of a rectangle rea of a parallelogram = ½ x b x h or ½bh or bh = b x h or bh = b x h or bh (Same as a rectangle) rea of a trapezoid = ½ x (b 1 + b ) x h or ½(b 1 + b )h or (b 1 + b )h rea of a kite = ½ x d 1 x d or ½d 1 d or d 1 d triangle rectangle parallelogram trapezoid kite
2 rea of a Triangle Formula: ½ x base x height or ½ b x h or ½ bh The base is measured by length The height is measured by length The height and the base must form a angle. ase= 8 inches Height = 9 inches angle is a right angle. When two lines form a angle they are perpendicular. ½ 8x9 = 36 rea = 36 in. rea of a Rectangle Formula: base x height or b x h or bh Height = 9 inches rea of a Parallelogram Formula: base x height or b x h or bh 1 x 8 = 96 rea = 96 in. Height = 8 inches ase= 1 inches *Use the same formula as a rectangle rea of a Trapezoid Formula: rea = ½ (base 1 + base ) x height = ½ ( b 1 + b ) x h = ½ (9+ 1) x 8 = 84 cm ase= 1 inches The base and the height must be perpendicular. Perpendicular= two lines form a right angle. ( ) ase x height = rea 1 x 9 = 108 rea = 108 in. height (8cm) base 1 (9cm) base (1cm) rea of Kites rea of a ircle Using Radius Formula: rea = ½ diagonal 1 x diagonal d 1 = (9cm + 11cm) d = (8cm + 8cm) = ½ x d 1 x d = ½ x 0 x 16 = 160 cm 8 cm 9 cm 8 cm diagonal 1 Radius () Diameter The area of a kite is half the product of the diagonals. Note: This formula works for the area of a rhombus as well, since a rhombus is a special kind of kite. Note that the diagonals of a kite are perpendicular. 11 cm diagonal Formulas: rea = π x radius or = πr rea = π x ( ) or = π(7 ) rea = π x 49 = 49 π = 154 cm.
3 Formula Key for ircles Diameter is x radius. (r) It is a line segment that divides a circle in half. Each half is called a semicircle. The diameter crosses through the center point. Diameter Diameter The radius is ½ the diameter. (½ d) It is a line segment with one end point on the center and one end point on the edge of the circle. circle can have many radii. E Radius D Radius, D, Equations to find Diameter & Radius Radius = 7cm. Diameter= 14 cm x radius = diameter ½ x diameter=radius x 7 = d ½ x 14 = 7 d =14 r = 7 Diameter Diameter= 14 cm Radius= 7 cm Radius Formulas: diameter = x radius or r radius = ½ x diameter or ½d
4 ircumference Definition: The distance around the whole circle Radius Diameter Formulas: ircumference = π x diameter or = πd ircumference = x π x radius or = πr ircumference using diameter: Diameter= 14 cm. = πd or = 14π = 44 cm. ircumference using radius: Radius = 7cm. = x π x r, = πr, = 14π, = 44 cm. Radius Diameter Radius Diameter Formulas: ircumference = π x diameter or = πd ircumference = x π x radius or = πr Formulas: ircumference = π x diameter or = πd ircumference = x π x radius or = πr
5 rea of a ircle rea of a ircle Using Radius Radius Diameter Radius () Diameter Formulas: rea = π x radius or = πr rea = π x (½ diameter) or = π(½d) rea of a ircle Using Diameter Formulas: rea = π x radius or = πr rea = π x ( ) or = π(7 ) rea = π x 49 = 49 π = 154 cm. Major and Minor rcs The Symbol is Radius Radius () Formulas: rea = π x (½ diameter) or = π(½d) rea = π x (½14 cm. ) or = π(7 ) rea = π x 49 = 49 π = 154 cm. Diameter (14 cm.) The minor arc is less than The major arc is more than D is a minor arc D = DE is a major arc. DE = DE = 35 0 E D Diameter What does E equal? = Note- The major arc will have three vertices to show direction.
6 Interior ngles of shapes & Lines Straight Lines Triangles The angles that make up a line always equal 180 degrees. X Y The interior angles of a triangle always equal 180 degrees. Y <X+ <Y = 180 <Y+ <Z= 180 <Z+ <Q= 180 <Q+ <X= 180 Q Z X+ Y+ Z = 180 X Z ngles The symbol for an angle is < 35 0 ngles are measured in degrees. The symbol for degrees is _ 0 Examples: (ngle ) < = 35 0 (ngle ) < = 65 0 (ngle ) < = 80 0 The sum (total) of interior (inside) angles of a triangle is always = Quadrilateral The interior angles of a Quadrilateral (4 sided shape) always equal 360 degrees. X+ Y+ Z + Q = 360 X Q Y Z Quadrilaterals (Squares, etc) ( Quadrilateral has 4 straight sides) Divide the shape into triangles : Formula: 180 (n-)= (4-)= ()= = 360 Square adds up to = 360 Let's tilt a line by still adds up to 360! quadrilateral can be divided into two triangles. Each triangle has 3 angles that add up to. X =
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