Tue. Aug 2nd, 2022

    Geometry Formulas

    Formulas for geometry, related to area and perimeter of triangles, rectangles, cercles, sectors, and volume of sphere, cone, cylinder are presented. Here are Geometry Formulas for perimeter, circumference, area, surface area, and volume. Scroll down the page for more examples and solutions using the geometry formulas.

    Right Triangle and Pythagora’s theorem

    Pythagora’s theorem: The two sides a and b of a right triangle and the hypotenuse c are related by

    a 2 + b 2 = c 2

    Right Triangle

    Area and Perimeter of Triangle

    Triangle

    Perimeter = a + b + c

    There are several formulas for the area.

    If the base b and the corresponding height h are known, we use the formula

    Area = (1 / 2) * b * h.

    If two sides and the angle between them are known, we use one of the formulas, depending on which side and which angle are known

    Area = (1 / 2)* b * c sin A

    Area = (1 / 2)* a * c sin B

    Area = (1 / 2)* a * b sin C .

    If all three sides are known, we may use Heron’s formula for the area.

    Area = sqrt [ s(s – a)(s – b)(s – c) ] , where s = (a + b + c)/2.

    Area and Perimeter of Rectangle

    Rectangle

    Perimeter = 2L + 2W
    Area = L * W

    Area of Parallelogram

    Parallelogram
    Area = b * h

    Area of Trapezoid

    Trapezoid
    Area = (1 / 2)(a + b) * h

    Circumference of a Circle and Area of a Circular Region

    Circle

    Circumference = 2*Pi*r
    Area = Pi*r 2

    Arclength and Area of a Circular Sector

    Sector

    Arclength: s = r*t

    Area = (1/2) *r 2 * t

    where t is the central angle in RADIANS.

    Volume and Surface Area of a Rectangular Solid

    Sector

    Volume = L*W*H
    Surface Area = 2(L*W + H*W + H*L)

    Volume and Surface Area of a Sphere

    Sphere

    Volume = (4/3)* Pi * r 3
    Surface Area = 4 * Pi * r 2

    Volume and Surface Area of a Right Circular Cylinder

    circular cylinder

    Volume = Pi * r 2 * h
    Surface Area = 2 * Pi * r * h

    Volume and Surface Area of a Right Circular Cone

    right cone
    Volume = (1/3)* Pi * r 2 * h
    Surface Area = Pi * r * sqrt (r 2 + h 2)

    Questions and Answers For Geometry Formulas

    1. A rectangle has a perimeter of 320 meters and its length L is 3 times its width W. Find the dimensions W and L, and the area of the rectangle.

    Solution and answer:

    • Use the formula of the perimeter to write.
      2 L + 2 W = 320
    • We now rewrite the statement “its length L is 3 times its width W” into a mathematical equation as follows:
      L = 3 W
    • We substitute L in the equation 2 L + 2 W = 320 by 3 W.
      2(3 W) + 2 W = 320
    • Expand and group like terms.
      8 W = 320
    • Solve for W.
      W = 40 meters
    • Use the equation L = 3 W to find L.
      L = 3 W = 120 meters
    • Use the formula of the area.
      Area = L W = 120 * 40 = 4800 meters 2

    2. The perimeter of a rectangle is 50 feet and its area is 150 feet 2. Find the length L and the width W of the rectangle, such that L > W.

    Solution and answer:

    • Use the formula of the perimeter to write
      2 L + 2 W = 50
    • and the formula of the area to write
      L W = 150
    • Divide all terms in the equation 2 L + 2 W = 50 by 2 to obtain
      L + W = 25
    • Solve the above for W
      W = 25 – L
    • Substitute W by 25 – L in the equation L W = 150
      L(25 – L) = 150
    • Expand the above equation and rewrite with right term equal to zero.
      -L 2 + 25 L – 150 = 0

    Sources: Wikipedia