Maths Project Work

Ashwani Class- XTH B Roll no. 50 Miss Meenu Presented by- Submitted To- Miss Meenu

Rectangle: Area = Length X Width A = lw Perimeter = 2 X Lengths + 2 X Widths P = 2l + 2w Parallelogram Area = Base X Height a = bh Triangle Area = 1/2 of the base X the height a = 1/2 bh Perimeter = a + b + c (add the length of the three sides)

Circle The distance around the circle is a circumference Circle The distance around the circle is a circumference. The distance across the circle is the diameter (d). The radius (r) is the distance from the center to a point on the circle. (Pi = 3.14) More about circles. d = 2r c = pd = 2 pr A = pr2 (p=3.14) Rectangular Solid Volume = Length X Width X Height V = lwh Surface = 2lw + 2lh + 2wh

Cylinder Volume = pr2 x height V = pr2 h Surface = 2p radius x height S = 2prh + 2pr2 Cones Volume = 1/3 pr2 x height V= 1/3 pr2h Surface = pr2 + prs S = pr2 + prs =pr2 + pr Sphere Volume = 4/3 pr3 V = 4/3 pr3 Surface = 4pr2 S = 4pr2

CIRCLE FORMULAS Circumference   = 2 • π •r Radius   =   π • diameter Area of Circle   =   πr²         = ¼ • π • d²

CYLINDER FORMULAS VOLUME= p.r2.h C.SURFACE AREA=2.p.rh T.SURFACE AREA=2.p.r.h

The area of this rectangle is lw. The most basic area formula is the formula for the area of a rectangle. Given a rectangle with length l and w, the formula for the area is A = lw  (rectangle). That is, the area of the rectangle is the length multiplied by the width. As a special case, the area of a square with side length s is given by the formula A = s2  (square). The formula for the area of a rectangle follows directly from the basic properties of area, and is sometimes taken as a definition or axiom. On the other hand, if geometry is developed before arithmetic, this formula can be used to define multiplication of real numbers.

A = bh (parallelogram). Dissection formulae Most other simple formulae for area follow from the method of dissection. This involves cutting a shape into pieces, whose areas must sum to the area of the original shape. For example, any parallelogram can be subdivided into a trapezoid and a right triangle, as shown in figure to the left. If the triangle is moved to the other side of the trapezoid, then the resulting figure is a rectangle. It follows that the area of the parallelogram is the same as the area of the rectangle: A = bh  (parallelogram). Two equal triangles. However, the same parallelogram can also be cut along a diagonal into two congruent triangles, as shown in the figure to the right. It follows that the area of each triangle is half the area of the parallelogram: Similar arguments can be used to find area formulae for the trapezoid and the rhombus, as well as more complicated polygons.

A = 4πr2 (sphere). Surface area of cylindrical Archimedes showed that the surface area and volume of a sphere is exactly 2/3 of the area and volume of the surrounding cylindrical surface. Most basic formulae for surface area can be obtained by cutting surfaces and flattening them out. For example, if the side surface of a cylinder (or any prism) is cut lengthwise, the surface can be flattened out into a rectangle. Similarly, if a cut is made along the side of a cone, the side surface can be flattened out into a sector of a circle, and the resulting area computed. The formula for the surface area of a sphere is more difficult: because the surface of a sphere has nonzero Gaussian curvature, it cannot be flattened out. The formula for the surface area of a sphere was first obtained by Archimedes in his work On the Sphere and Cylinder. The formula is A = 4πr2  (sphere). where r is the radius of the sphere. As with the formula for the area of a circle, any derivation of this formula inherently uses methods similar to calculus.

Additional formulae Areas of 2-dimensional figures Triangle: (where B is any side, and h is the distance from the line on which B lies to the other vertex of the triangle). This formula can be used if the height h is known. If the lengths of the three sides are known then Heron's formula can be used: (where a, b, c are the sides of the triangle, and ,

Basic Proportionally Theorem If a line drawn parallel to one side of a triangle to intersect the other two sides in a distinct points, the other two sides are divided in the same ratio. AD/BD=AE/EC

In a right triangle, the sum of perpendicular is equal to the PYTHAGORAS THEORM In a right triangle, the sum of square of the base and perpendicular is equal to the square 0f hypotenuse A b c

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