AREAS AND VOLUMES.

Slides:



Advertisements
Similar presentations
Area and Perimeter By Christine Berg Edited by V T Hamilton.
Advertisements

ERT252/4 GEOMATICS ENGINEERING
Geology and Surveying (Part B - Surveying) Volumes and DTMs
ENGINEERING SURVEYING & PHOTOGRAMMETRY CVE 314
11 – 6f Area, Surface Area & Volume
11.1 Understanding Area. Units of measure 1.Linear units: perimeter, circumference 2.Square units: area 3.Cubic units: volume Definition: The area of.
Finding the Volume of Solid Figures MCC6.G.2 – Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes.
1. A kite has two diagonals. We’ll label them. 2. The diagonals in a kite make a right angle. 3. Let’s put a rectangle around the kite because we know.
Geometry.
Parallelograms, Trapezoids and Triangles Section
Areas of Parallelograms. Parallelogram A parallelogram is a quadrilateral where the opposite sides are congruent and parallel. A rectangle is a type of.
By Ricardo Garcia. perimeter  Square p=4s  Rectangle p=2l+2w or p=2(l+w)
Area of Quadrilaterals and Triangles. What is a quadrilateral? Any polygon with four sides and four vertices (or corners) All sides must be straight.
Volumes of Pyramids & Cones
Lecture 19 – Numerical Integration 1 Area under curve led to Riemann sum which led to FTC. But not every function has a closed-form antiderivative.
Areas of Triangles, Parallelograms, & Trapezoids.
Camilo Henao Dylan Starr. Postulate 17 & 18 Postulate 17: The area of a square is the square of the length of a side (pg.423) A=s 2 Postulate 18 (Area.
Quiz Review 11-1 to Match each with the correct formula. (Hint: One answer is used twice) B C A B E D.
Areas and Volumes Introduction Faculty of Applied Engineering and Urban Planning Civil Engineering Department 2 nd Semester 2008/2009 Surveying.
Reflections 30 Reflect across y=x (x,y)  (y,x) Reflect across x-axis (x,y)  (x,-y) Reflect across y-axis (x,y)  (-x,y) Reflect across y=x Reflect across.
Warm-Up What are the 8 Standards of Mathematical Practices? Make sense of problems and persevere in solving them Reason abstractly and quantitatively Construct.
What is the formula for area of rectangle? What is the formula for the surface are of a rectangle? What is the formula for the volume of a rectangular.
11-1 Areas of Rectangles and squares. Formulas 1) Area of rectangle = base x height or length X width 2) Area of square = (side) 2 or base X height 3)
Area Measurements.
Copyright©amberpasillas2010 Area of Irregular Figures.
Area of a Parallelogram
10-2 Areas of Trapezoids, Rhombuses & Kites Objective: To find the area of a trapezoid, rhombus or kite Essential Understanding You can find the area of.
10-1: Area of Parallelograms and Triangles Objectives: To find the area of parallelograms and triangles To find the area of parallelograms and triangles.
MG 2.1: PERIMETER & AREA RECTANGLES, SQUARES, TRIANGLES, CIRCLES Defining and calculating.
Vocabulary: Area— amount of space _________________________ a plane figure. Measured in ______________ units. Perimeter— __________________________________.
Class Notes Geometry Sec 2.7 Objective: Apply concepts of perimeter, area, and volume 1.Review: Find the perimeter of each figure below a. 4x -
Areas of Parallelograms and Trapezoids Objective: Learn to find the area of parallelograms and trapezoids.
Make a Model A box company makes boxes to hold popcorn. Each box is made by cutting the square corners out of a rectangular sheet of cardboard. The rectangle.
square rectangle parallelogram trapezoid triangle.
Calculating Bulk Earth Works Simpson's Rule. Simpson’s Rule Sum of Grids Method Trapezoidal Method All assume that the land is a straight line between.
Finding the Area of Polygons Rectangles Parallelograms Triangles Trapezoids.
USE OF PLANIMETER,COMPUTATION OF VOLUME FROM CROSS SECTION
Formulas. Demonstrate a 2 + 2ab + b 2 = (a + b) 2 Find the area of the big square by adding up the areas of the 2 squares and 2 rectangles: a 2 + ab +
Area of Parallelograms
VOLUME of PYRAMIDS Consider a pyramid and a prism having equal heights and bases with equal areas. If the pyramid is filled with sand and its contents.
Triangles, Quadrilaterals, Nets, Prisms & Composite Polygons
Area of Trapezoid.
How do you calculate the area of squares and rectangles?
Calculating Cut and Fill
9-1 C and D: Area of Triangles and Trapezoids
Area and Perimeter 6th grade math.
Areas of Triangles and Special Quadrilaterals
Area and Volume Area is the amount of space contained in a two-dimensional figure Volume is the amount of space in a three-dimensional figure.
Long sections eg road cuttings Deep sections eg basement excavations
Trial and Improvement 100 cm2 Example
1-5 Geometric Formulas Polygons
Visit for more Learning Resources
Areas Regular Figures Mathematical Formulae Method of Coordinates
Calculate Area of Composite Shapes
Area of Parallelogram.
Finding the Volume of Solid Figures
Introduction Persons engaged in surveying are often called to determine volumes of various types of material. The most common unit of volume is cubic having.
ADVANCE SURVEYING.
Area of Parallelograms and Trapezoids
AREAS AND VOLUMES.
Introduction Persons engaged in surveying are often called to determine volumes of various types of material. The most common unit of volume is cubic having.
Difference of Two Squares
Area of Composite Figures
Introduction Persons engaged in surveying are often called to determine volumes of various types of material. The most common unit of volume is cubic having.
Areas of Parallelograms and Trapezoids
Substitution 3..
1) Expand Brackets 2) Factorise
Chapter 6 Construction Quantity Measurement
Presentation transcript:

AREAS AND VOLUMES

Mathematical formula for area calculation: Area= ½( b×h ) Area = ½ (a ×c ×sinB ) Area =√s(s-a)(s-b)(s-c) s=(a+b+c)/2 Area = a² Area = a×b Area=π r² Area = ½ ((a+b)/2)h Area=1/4 n.a² cot(180º/n) Area=π(r2² - r1²) Area=(∆ / 360).π.r² Area = ½ r²((π∆/180)-sin∆) Area= 2/3 .b .h Area= π.a.b

Areas by the method of coordinates: x y Y1x2 x1y2 Y2x3 x2y3 Y3x4 x3y4 Y4x5 x4y5 Y5x1 x5y1 x Area = ½ ( (y1x2 + y2x3+ y3x4 + y4x5 + y5x1) – (x1y2 + x2y3 + x3y4 + x4y5 + x5y1)) = ½ ( x1(y5-y2) + x2(y1-y3) + x3(y2-y4) + x4(y3- y5) + x5( y4-y1) )

x y x y

Areas of irregular figures: Trapezoidal rule:

Simpson’s one-third rule:

Calculation of volumes: All highways and railroad construction projects involve Earthworks( Cut & Fill ) There are two methods to calculate the volumes of cut and fill.

Average End Area Method (AEA):

Volume By Prismoidal Formula:

Volume From Contour Maps The figure

Volume From Spot Levels The following figure Volume (V) = (A / 4)(∑h1 + ∑2h2 + ∑3h3 + ∑4h4 ) where A is the area of one rectangle or square and h1,h2,h3,h4 are the corner heights common to one, two, three and four rectangles respectively. Solution