Posted by PAT on Wednesday, April 6, 2011 at 5:13am.
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  MathMate, Wednesday, April 6, 2011 at 7:47am
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*23*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.
Answer This Question
Related Questions
 geometry  Find the area of a pentagon ABCDE with verticles A(0,4),B(3,2),C(3,1...
 geometry  A pentagon ABCDE. EG drawn parallel to DA meets BA produced at G and ...
 Geometry  Regular pentagons A and B are similar. The apothem of Pentagon A ...
 geometry  In the diagram, ABCDE is a regular pentagon with the measure of ...
 Geometry  Problem: ABCDE$\ is an equilateral pentagon with side length 2 in ...
 maths  The convex pentagon ABCDE has a right angle at B,AB=BC andCD=DE=EA=1cm,...
 Geometry  (SAT Prep) The perimeter of pentagon ABCDE is 30 in, AB = 7 in, BC...
 pentagon...GEOMETRY  ABCDE is a regular pentagon. FAD is an equilateral ...
 Math  the area of ABCDE is 18 sq. cm.; the area of a similar pentagon PQRST is ...
 Algebra Grade 7  Pentagon ABCDE ~ Pentagon FGHIJ. Find BC for GH =12, IJ = 15 ...
More Related Questions