Area—number of square units enclosed Dimensions must all be the same unit Altitude/Height—line perpendicular to the base with triangles, parallelograms, or trapezoids
Square/Rectangle Perimeter (distance around) P = 4 x S (square) P = 2 L + 2 W Area A = L x W (rectangle) A = S x S (square)
Circles (1/2 diameter) Area Radius A = ∏ r ² or ∏ x r x r Diameter Circumference C = ∏ x d
Parallelogram A = b x h Triangle A = ½ b x h
Trapezoid A = ½ h(b1 + b2) *or you can treat the trapezoid like a composite figure by dividing it into simpler figure and finding the area then adding the totals
Circles Area -- A = ∏r² Circumference -- C = ∏d or 2r∏
3-D figures are also called space figures or solids Vertex-where lines meet at a point Base-flat surface on the top and bottom of the figure Base edge-lines along the base Lateral face-flat surface on sides of the figure Lateral edge-lines along the sides of the figure
Prism-2 parallel bases are congruent polygons and lateral faces are rectangles sides are always rectangles base (can be any shape; same on both ends) Pyramid-1 polygon base the lateral faces are triangles vertex sides are always triangles base (can be any shape)
Cylinder-2 parallel bases that are congruent circles base (always a circle) sides are rounded Cone-1 circular base and 1 vertex vertex base (always a circle) Sphere-all points equal distance from center
Net—pattern you can form into a space figure Named for the bases You must know what shape the bases and faces form to be able to figure out a net
CylinderTriangular Prism
CubeRectangular Pyramid
Square Root– the inverse of squaring a number Symbol √ The square of an integer/number is a perfect square On calculator: 2 nd button then x² button then # then enter Irrational Number—decimal form of a number that neither terminates or repeats If an integer isn’t a perfect square, its square root is irrational
The first 13 perfect squares are easy to memorize: 0² = 06² = 36 1² = 17²= 49 2² = 48² = 64 3² = 99² = 81 4² = 1610²= 100 5² = 2511² = 121 6² = 3612²= 144 * a square is a number times itself
Practice : (simplify & state whether it is rational or irrational) 1.) √64 2.) √100 3.) - √16 4.) - √121 5.) √27 6.) - √72 7.) - √50 8.) √2
Volume—number of cubic units needed to fill in a 3-D figure Cubic unit—space occupied by a cube This is why the units are cubed
Rectangular Prism or Cube V = L x w x h Cylinder V = ∏r 2 x h
Volume of Triangular V = (1/2 b x h) x h Prism Or V = b x h x h Volume of a Cone or Pyramid 2 Pyramid V = 1/3 ( L x w) x h Or V = l x w x h 3 Cone V = 1/3 (∏ r 2 ) x h Or V = ∏r² x h 3
Surface Area (S.A.)—sum of the area of the bases and the lateral sides of a space figure Draw the figure Fill in all of the numbers for the edges Find area of each face and add everything together Sometimes it helps to draw a net figure then fill in the numbers
Find each of the following areas: L x w L x h w x h Then add up all areas and multiply answer by 2 S.A. = l x w = 6 l x h = w x h = 5 sum = ? x 2 7 answer = ?
*find area of circle then find area of rectangle add *formula for area of rectangle is (∏d x h) Area of the circle: A = ∏ r 2 Ex: A = h= 11.5 cm A = ? X 2 Area of the rectangle : A = ∏ x d x h A = R = 3.5 cm A = ? Total Area = ? *
EX: Area of Triangle: A = ½ b x h A = ½ (6 x 4) A = ? X 2 5 cm 6 cm5 cm Area of Rectangle: A = l x w 6 cm 12cm A = 12 x 5 4 cm A = ? X 3 * There are 3 rectangle so multiply that area by 3 * There are 2 triangles so multiply that area by 2 Total Area = ?
Ex: Area of Rectangle: A = l x w A = 12 x 12 A = ? 12 m 16 mArea of the Triangle: A = ½ b x h 12 m A = ½ (12 x 16) A = ? There are 4 triangles so multiply the area of the triangle by 4. Then add the area of the rectangle to the areas of the triangles. Total Area = ?
Ex: Area of the Triangle: A = ½ b x h A = ½ (8 x 10) 10 m A = ? 14 cm Area of the Circle: A = ∏ r 2 A = 3.14 x 7 2 A = ? Add the areas of the circle and the triangle. Total Area: ?
Ex: S.A. = 4∏ r 2 d = 5 in S.A. = 4 x 3.14 x S.A. = ?