geometry

posted by .

Find the area of a pentagon ABCDE with verticles A(0,4),B(3,2),C(3,-1), D(-3,-1) and E (-3,2)

  • geometry -

    If the pentagon's boundary does not cross itself, I would use the surveyor's formula:
    1. lay out the coordinates in order, repeat the first at the end.
    A(0,4)
    B(3,2)
    C(3,-1)
    D(-3,-1)
    E (-3,2)
    A(0,4)

    2. Cross multiply between each successive pair and sum.
    For A and B, we get 0*2-3*4=-12
    For B and C, we get 3*-1 - 3*2 = -9
    Continue until the last pair.
    The sum of all 5 products is twice the area. If the vertices have been named clockwise, the sum will be negative.

    3. Divide the sum by 2. If the sum is negative, write down only the positive value.

    For the example:
    vertex sum
    A -12
    B -9
    C -6
    D -9
    E -12
    Sum -48
    Area = 48/2=24

    Check my calculations.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. geometry

    In the diagram, ABCDE is a regular pentagon with the measure of represented by 2x + 1. If the perimeter of the pentagon is 45, find the value of x.
  2. geometry

    A pentagon ABCDE. EG drawn parallel to DA meets BA produced at G and CF drawn parallel to DB meets AB produced at F. Prove that the area of pentagon ABCDE is equal to the area of triangle GDF.
  3. geometry

    Find the area of a pentagon ABCDE with verticles A(0,4),B(3,2),C(3,-1), D(-3,-1) and E (-3,2)
  4. Algebra Grade 7

    Pentagon ABCDE ~ Pentagon FGHIJ. Find BC for GH =12, IJ = 15 and DE = 10
  5. pentagon...GEOMETRY

    ABCDE is a regular pentagon. FAD is an equilateral triangle, such that points F and E are on the same side of line AD. What is the measure (in degrees) of ∠FAB?
  6. maths

    The convex pentagon ABCDE has a right angle at B,AB=BC andCD=DE=EA=1cm,AC=2cm.If AC and ED are parallel ,find the area of the pentagon.
  7. Math

    the area of ABCDE is 18 sq. cm.; the area of a similar pentagon PQRST is 32 sq.cm. the diagonal AC is 6 cm.; find the length of PR.
  8. Geometry

    Regular pentagons A and B are similar. The apothem of Pentagon A equals the radius of Pentagon B. Compare the areas. The area of Pentagon A is equal to 1.49 times the area of Pentagon B. The area of Pentagon B is equal to 1.49 times …
  9. Geometry

    Problem: ABCDE$\ is an equilateral pentagon with side length 2 in which angle B= angle E=120 degrees. The area of ABCDE can be expressed in the form square root of x + square root of y for some integers x and y. Find x+y. I don't understand. …
  10. Geometry

    (SAT Prep) The perimeter of pentagon ABCDE is 30 in, AB = 7 in, BC = CD = 6 in, DE = 5 in. How many sides of the pentagon have equal length?

More Similar Questions